How smart is /b/?
The stories and information posted here are artistic works of fiction and falsehood.
Only a fool would take anything posted here as fact.
Only a fool would take anything posted here as fact.
How smart is /b/?
>>701433258
>regular coins
>posts monopoly money
>>701433462
>worth more than Amerifat burger money
75% ?
Depends:
If we flip both and both land tails is one magically flipped to heads or is one guaranteed heads? it will either be 25% or 50% depending
50% - If one of them is definitely heads, technically you're only flipping 1 coin, and that leaves you with 50/50 chance
>>701433258
50% you fucking retard
how is this even a question
>>701433673
This? Im not very smart but: 1 lands heads, thus 50 percent of the task completed. The 2nd coin has a 50% chance to land heads so it gives u a 75% chance that both of the coins will land heads, assuming one has landed heads. But if the one coin always lands heads then shouldnt it really be 50%?
Conditional probability only works when events are not independent. In that case P[B|A] = P[B]
>>701433673
>>701433715
>>701434033
>3
>what is the probability that at least one landed heads
>given one of them landed heads
>one of them is already heads
"what is the probability of a coin landing heads" is now the question
the answer to which is 50%
jesus
![new%20mcdonalds[1].gif](https://i.imgur.com/shOn0VG.gif "new%20mcdonalds[1].gif")
Two (I assume fair) coins were flipped, at least one was heads. This are the possible outcomes
HH
HT
TH
(not TT, since at least one head)
since we have three options, and only one options gives to heads, the probability is 1/3.
>>701434334
>Dependent
>>701434373
>one of them is already heads
there are 3 different ways for two coins to be "one is already heads". HT, TH, HH. of the 3 ways for two coins to be "one is already heads", one of those is HH.
>answer is 1/3
>>701433258
50%
>>701434557
2 of those are the same option dipshit
33.33333%
>>701434557
stop trying to sound smart idiot, TH and HT are the same because the coins are the same
50 fucking percent
7
If P(A|B) = P(A), then events A and B are said to be independent. In such a case, having learned about the event B does not change our knowledge about the event A. Also, in general, P(A|B) (the conditional probability of A given B) is not equal to P(B|A). For example, if you have cancer you might have a 90% chance of testing positive for cancer. In this case what is being measured is that the if event B "having cancer" has occurred, the probability A - test is positive given that B having cancer occurred is 90%, P(A|B) = 90%. Alternatively, you can test positive for cancer but you may have only a 10% chance of actually having cancer because cancer is very rare. In this case what is being measured is the probability of the event B - having cancer given that the event A - test is positive has occurred, P(B|A) = 10%. Falsely equating the two probabilities causes various errors of reasoning such as the base rate fallacy.
>>701434864
Prove it. You can't just say things.
Anyone saying 50%, please kill yourselves or at least never have kids.
The answer is 1/3.
For a 2 coin flip, there are 4 equally probable outcomes:
Heads - Heads
Heads - Tails
Tails - Heads
Tails - Tails
At least 1 coin landed heads, so Tails - Tails is no longer possible, leaving 3.
HH
HT
TH
HH is 1 of those 3
1/3
>>701434864
>>701434999
if you want to combine the two options into one, then you have to combine their probabilities as well!
HH - 1/3
HT - 1/3
TH - 1/3
combine into
HH - 1/3
TH OR HT - 2/3
and the answer is still 1/3
75%.
Heads/Heads - Can be.
Heads/Tails - Can be.
Tails/Heads - Can be.
Tails/Tails - Can't be.
Anyone who argues otherwise is a complete fucking retard and should go back to school.
we hAve coins a and b
being heads =h and tail =t we have the following possibilities
ah bh
ah bt
at bh
so it's a 2/3 or 66% of a and b not being heads at same time
>>701435310
Fuck, anon, that's freaky.
>>701435425
you're wrong in so many levels
>>701435618
>Fuck, anon, that's freaky.
Are you 12 years old?
Fucking spergs. Trick question.
The probability that two independent events BOTH happen is product rule. So P(A) and P(B) occuring is P(A)*P(B).
> P(A) = 0.5 ; P(B) = 0.5.
> P(A) * P(B) = 0.25. [two fair coins both heads]
The question is asking, what is the probability given that one of them is known to be heads?
Well, these are independent events (one does not influence the next), so it's exactly the same. P(B) is the same 50%, but both occuring is 25%.
>>701433258
It's 33,333...%, 1/3 possible outcomes, the outcomes being tails/tails, tails/heads, heads/heads.
50%
Christ. Thanks common core.
>>701436003
>Trick question.
No. It's a basic conditional probability math question, you underaged faggot.
Conditional Probability:
Probabilty of Event A given Event B
Use Bayes' theorem.
A = "both coins are heads"
B = "at least one coin is heads"
P(A|B) = P(A∩B)/(P(B)) = (1/4)/(3/4) = 1/3
So many morons in this thread.
For all you fuckers saying it's 1/2, I'm really not sure if you're trolling or just being thick as shit.
The question doesn't say "assuming coin #1 has landed heads" (call this scenario 1), it says "assuming at least one coin has landed heads" (scenario 2). In this explanation, HT means "coin 1 lands heads and coin 2 lands tails".
Normally when tossing two coins you have four outcomes:
HH
HT
TH
TT
In the case of scenario 1, you have two possible outcomes:
HH
HT
We can ignore TH and TT because we KNOW for a fact that coin 1 landed heads. Therefore there are 2 outcomes, 1 of which is HH, so the answer is 1/2
In scenario 2, you have three outcomes:
HH
HT
TH
We can ignore TT, as we know at least 1 coin landed heads. So we have 3 outcomes, 1 of which is HH, so it's 1/3.
>>701434789
Mathematically 2 of those are the same, idiot.
Here
One is heads. It is removed from future of equation. As it is a definite H.
You are now left with H or T.
The answer is 1/2, .5, or 50%
You're all stupid.
>>701433616
C O I N S
O
I
N
S
>>701436780
>Mathematically 2 of those are the same
You're retarded.
Now think about it again until you figure out how you are wrong.
Protip: Imagine using a penny & quarter as the 2 coins.
>>701437075
Confirming 1/3
>>701437134
>One is heads. It is removed from future of equation.
No, try again.
There are four different combination that one flip with two coins can produce.
heads, heads
tails, tails
tails, heads
heads, tails
(yes you differentiate the last to combinations since both coins got a heads and a tails side)
therefore the chance of getting double heads is one out of four or 25%
Now given that one coin already landed on head the chances are changing because there are only two possible combinations left:
heads, heads
heads, tails
therefore the chance is one out of two or 50%
>>701437531
That doesn't change the probability you fucking ape.
>>701436473
> Conditional
> Bayes' Theroem
AHAHAH you're serious. No fundamentals.
Using Bayes, TH and HT are separate events. You might as well be crossing off TH because "the first one was heads". Then you know what you get? 50%.
Conditional table is the ruse, HT and TH are not separable events, its:
> BOTH H
> ONE H ONE T
> [xxxxBOTH Txxxx] crossed out.
This is an elementary ruse in combinatorics. Treating combined independents as conditionals. You fell for it.
Underage faggot? I have an M.S. in biochem you gook. Get off my bengalese carpentry board.
>>701433258
Idk, I'm bad at social studies
>>701437075
>>701436632
>>701437743
fucking faggots stop treating TH and HT as different events, goddamn retards
>>701433258
The question is not just the probability that both landed heads (25%), it's the probability that both landed heads _given_ that at least one of them landed heads.
>>701437838
YOU ARE SO FUCKING CLOSE YOU DUMB NIGGER
>>701436473 That mathage will come in handy while you're flippin' burgers, kiddo
>>701433258
It depends. Are these feminist coins we're talking about?
Those always land on their face.
>>701438305
correct me faggot
>>701438150
They ARE different events. The two coins are different.
>>701438150
But they are.
If coin 1 is a quarter and coin 2 is a penny, then HT and TH are different events - HT is a heads on the quarter and a tails on the penny, and TH is a tails on the quarter and a heads on the penny - DIFFERENT EVENTS
>>701433258
1/3
This thread makes me worry about the future of our species.
Anyone saying 1/3, please kys to save the future
>>701438150
What's it like being retarded, anon?
>>701438428
Given that AT LEAST ONE COIN (note it doesn't specify WHICH coin, just A coin) landed on heads leaves you with HH, HT and TH
>>701438646
no because coin A is fixed on heads you dumb fuck.
>>701434898
Correct.
>>701437838
>Now given that one coin already landed on head the chances are changing because there are only two possible combinations left:
Nope. Only tails, tails is ruled out, leaving 3
heads, heads
heads, tails
tails, heads
1/3
Revise your solution and correct your mistake.
>>701437843
>That doesn't change the probability
I know. The answer is 1/3.
>>701438823
COIN A ISN'T FIXED, WHY ARE YOU SO FUCKING RETARDED
>>701439003
Learn to read you god damn idiot, are you too stupid to understand op's picture?
>>701437862
>"the first one was heads".
Question never says that, read it again.
If the FIRST coin landed heads, the probability that both coins are heads is 1/2
If AT LEAST ONE coin landed heads, probability that both are heads is 1/3
Pic Related
Source: Slide 4 Washington University Math Dept
http://courses.cs.washington.edu/courses/cse312/11wi/slides/04cprob.pdf
I hope you didn't pay for your shit-tier education.
>the probability that both landed heads given that at least one landed heads.
It doesn't specify which coin landed heads. You only know that ONE has already been thrown and landed heads. Therefore, this leaves you with one coin to flip and a 50% chance of both landing heads.
There's really only one case here. You are currently evaluating for Y, knowing that X (order unspecified) is already heads. Y has a probablility of 50% each scenario. If you wanted to evaluate all possible cases you'd actually have:
xH
xT
Hx
Tx
Where x is definitely heads. So a 1/2 probability.
>>701438460
Nope. This is a run of the mill undergraduate combinatorics trick question. If it was worded "what is the probability that both landed heads given that the FIRST one landed heads", you would know to use Bayes / separate time-series. Because it's worded "what is P(HH) given that AT LEAST ONE landed heads", it combines the events. As if I was throwing two coins in one hand, TH and HT are the same event. This gives you 50% using conditional table, which is, not coincidentally, the probability of the second coin being heads.
>>701438463
Separating coins. Doesn't matter because of "AT LEAST ONE" trick in question. Nope.
>>701438616
I don't know, really, the real retards are those who can't ever accept that we can be wrong. What does that feel like, exactly?
>>701438463
>>701438823
You're retarded. No coin is fixed.
Answer = 1/3
It's 2/6 and if you think it's anything else you should die because their mother will die in her sleep tonight if you don't reply to this post
>>701439167
>at least one coin landed heads
means something sifferent to
>coin A is fixed as heads
You retarded nigger.
OP question allows for either coin to be tails, just not both simultaneously.
There are 3 equally probable outcomes that satisfy the condition of having at least one heads
heads - heads
heads - tails
tails - heads
1/3
Cry moar
I say it's 75 % due to Tree Diagram. (Worked on the goat problem too, so why not here.)
>>701439259
You still don't get it, lol. "the first one was heads" is in quotes because it shows the idea that these events are seperate time-series, I.E. conditional probability. "AT LEAST ONE" means HT and TH are the same event.
Still giving me conditional probability rules for an undergrad-tier question in combinatorics? Give me a break, fag. And no, I didn't pay a cent, full ride, thanks SAT. I hope you're paying for yours.
>>701439282
>You only know that ONE has already been thrown and landed heads. Therefore, this leaves you with one coin to flip and a 50% chance of both landing heads.
No. 2 coins were flipped ant AT LEAST ONE coin landed heads.
For a 2 coin flip, there are 4 equally probable outcomes:
Heads - Heads
Heads - Tails
Tails - Heads
Tails - Tails
At least 1 coin landed heads, so Tails - Tails is no longer possible, leaving 3.
HH
HT
TH
HH is 1 of those 3
1/3
>>701433258
> still falling for this thread
> literally takes longer to flip a coin than to just google the fucking answer
>>701439758
And if we now used this to give an answer to the actual question, the solution'd be 25%
>>701439776
>provides no math solution
>tells others they don't get it
top kek
You just got BTFO by University of Washington.
1/3
>>701439758
Because Monty Hall is an exercise in conditional probability. P(A) influences P(B) because the number of doors decrease. That's the only reason why it doesn't work.
For those who haven't got it yet
> Conditional(HH/HT/TH/TT) -> 0.75
> Independent(2H/1H1T) -> 50% or probability of flipping a coin.
Just FYI, my probability friendo.
>>701440125
lolwat
>>701439329
>conditional probability
>trick question
Never reproduce.
>>701440125
> Conditional(HH/HT/TH/TT) -> 0.75
> Independent(2H/1H1T) -> 50% or probability of flipping a coin.
Your post makes zero sense
>>701440125
I don't quite get the difference between conditional and independent yet. I mean, if you ask "How high's the probability to get two heads in a row", you also use tree diagrams to see 50%*50% = 25%. At least that's how we handled that in school.
>>701436473
you are fucking retarded.
http://math.stackexchange.com/questions/991060/flip-two-coins-if-at-least-one-is-heads-what-is-the-probability-of-both-being
> what is math
>>701440588
>provide math solution
>get called retarded
Sure thing, m80.
>>701433258
33%?
Forced myself to answer within 10 seconds or so
>>701433258
What is the probability that a coin never lands on anything but heads ever ever ever
The question is a weirdly worded math circle jerk, by asking the same question in different way the answer can be 1/2, 1/3 or even fucking 1/4
In this case, its 1/3
>>701441682
>by asking the same question in different way the answer can be 1/2
>same question
No. It would not be the same question.
Here is the OP question worded differently.
What is the answer?
protip: 1/3
>>701441956
>this
>>701441956
Lets ask it this way.
You flip 2 coins and see that 1 landed head before looking at the second coin, what is the probability of both landing heads?
Or
You flip 2 coins, 1 of which is a double headed coin, what is the probability of both landing heads?
Your question assumes that the coins are flipped at the same time and doesnt specify which of the coins was heads, while most people would assume you look at them 1 at a time, its a stupid question made to troll people into saying 1/2 so you can laugh at them.
>>701442391
You're asking a totally different question you fucking retard.
>>701433258
>ITT: people who don't realize both coins have landed already.
The answe is 50%
>>701442527
yes, but im asking the question most think YOU are asking, still dont get it?
>>701435173
>being this dumb
Your so stupid it hurts
>>701437134
*your
>OP clearly states one coin will always land on heads
>it suddenly becomes a question of "if I have a coin what are the chances it lands on heads if I flip it?"
>clearly 50%
Niggas what?
>>701442634
>most
I would hope not. The OP's wording is EXTREMELY transparent. The people here read it, processed it, and spat out an incorrect answer with confidence. There was no tricky wording or cheap tricks, it's just that most people aren't very smart when it comes to probabilities.
>>701433258
this doesnt measure smartness. It just tests whether someone can think in a technical or logical way. Its like saying: if youre bad at math then youre not smart.
>>701440257
>>701440305
>>701440560
I'm disappointed in you, Anon. You can't just keep giving me examples of conditional probability for this independent event. That's the whole point of this question.
>>701440582
Yes.
> probability of two heads = 0.25
> probability of two heads given -AT LEAST- one head: 0.5 (probability of a coin flip)
> probability of two heads given -THE FIRST- is head: 0.333~
>>701440092
Did you notice the words "the first" in that slide titled 'Cond_Prob'? I don't know how to tell you this, but it's just academic laziness. It's from the conditional probability unit, so they are using Bayes. You can see this exact same treatment, they make HT and TH separate events, meaning there is a difference between the "first head second tails" and "first tails second head", where these are forced to be the same instance by use of "at least". An oversimplification for undergrads where the nuances don't exist.
>>701442616
Thank you, Anon.
>>701438826
>>701434898
Incorrect
>>701433258
>>701435173
>>701434557
>>701436632
You guys are Retarded
HH
HT
TH
TT
Each Side has a 50% Chance of landing on Heads, you determine probability my multipling the two chances of each coin individually landing on heads together, which equals 25%. So out of two coins its a 25% chance of both landing on heads.
If we dismiss TT
HH
HT
TH
Each coin has a 66% Chance to land on heads, which multiplied together gets us 43.5%
No shit, everybody is wrong.
>>701443399
What the fuck, you... you can't be serious. Someone disprove this shit right now.
>>701443399
>An anon manages to prove the answer is literally in the middle between 50% and 33%
>>701443116
>it's just that most people aren't very smart when it comes to probabilities.
i agree and im saying you are using it to make people look stupid, less people would get it wrong if you made the question clearer as " one of them landed heads" isnt all that clear when it means you dont know which of the coins it was.
Ever tried flipping coins? you can actually see the results. My point stands, the question is unclear and looking at how this is /b/ after all, it was probably made with the intent to b8 people in to giving the wrong answer.
TH
HT
HH
One of these happened. What is the probability of it being HH? ... 1/3. Every other answer is a troll or stupid
>>701443399
>Each Side has a 50% Chance of landing on Heads
>If we dismiss TT
>Each coin has a 66% Chance to land on heads
He can't see how flawed his logic is. Let's point at him and laugh.
25 percent, get good retards.
The fact that one is flipped is unnescesary
>>701443869
What is the probability of it being HH if YOU KNOW that one of them is H already?
>>701443723
First of all I'm not the OP, and second of all the OP reads "atleast one of them landed heads", which is allot more transparent than just "one of them landed heads"
I kinda kinda kinda see where you're coming from with how there's no real life equivalent, but it's still a hypothetical math problem, and atleast when I was in school this was how all of our problems were worded.
>>701444182
but you dont know which one, it can still be HT OR TH along with HH ofc.
>>701433258
2/3 now fuck off
>>701443869
The Results per coin are
T
H
H
and
H
T
H
Which is a 66% Per coin that it'll land heads is it not?
>>701444182
I excluded TT. If I'm wrong please show me why I'd love to learn. I start learning probability this semester in one week
>>701434334
can you explain further? My math is sleeping right now
>>701444299
Well the people here dont know that its a hypothetical math problem, OP doesnt say it is.
>>701443869
I take two coins in my hand.
I throw them into a cardboard box, where my friend is watching.
He says, 'at least one is a head'.
It's either HH or HT. If I threw them one at a time, he could say "the first one was a head". That separates these events. That brings this close to the probability of 0.25, the chance of both. It would be 1/3.
But he said "at least one" is a head. What does that leave me with?
Either HH or HT. The position doesn't matter now, because there is no "first". So, the chance that both are heads, is 50%, the same probability as flipping a a fair coin. This makes sense intuitively: say I present you with a coin showing heads, and hand you a coin. What is the probability both will now be heads? 50%.
>>701444346
ONE LANDED HEADS
Is that enough for you?
One is heads, what are the odds of the one being heads as well?
>>701444406
Yeah I see that now. I need to do some thinking. I posted my answer before looking at yours (I assume it's one that got 43.5% as its answer)
>>701433258
1/4. ItMs asking probability that they both landed on heads, which is 25%. Given that at least one landed on geads is extra information
>>701433258
1/4. ItMs asking probability that they both landed on heads, which is 25%. Given that at least one landed on heads is extra information
Yeah, I see all you fucks saying it after I posted it, git gud retards
>>701433258
1/4. ItMs asking probability that they both landed on heads, which is 25%. Given that at least one landed on beds is extra information
>>701444827
33%
TH = 1/3
HT = 1/3
HH = 1/3
Its a hypothetical math circle jerk question made bate you into giving us the wrong answer so OP can laugh at you.
>>701433258
1/4. ItMs asking probability that they both landed on heads, which is 25%. Given that at least one landed on dreads is extra information
>>701442391
>You flip 2 coins and see that 1 landed head before looking at the second coin
That's a different question to the OP question. Answer to that is 1/2
>You flip 2 coins, 1 of which is a double headed coin
That is also a different question to the OP, and the answer is 1/2 there also.
>Your question assumes that the coins are flipped at the same time
Not really but it doesn't matter. They can be flipped simultaneously or sequentially. Answer will be the same either way.
> and doesnt specify which of the coins was heads
Exactly
>its a stupid question made to troll people into saying 1/2 so you can laugh at them.
Nah, anon. It's a pretty common basic conditional probability question in beginner stat/math classes.
Answer is 1/3
>>701444802
But isn't TH twice as common as HH in that scenario?
>>701445322
One of them will ALWAYS land heads. Why are there three outcomes there, retard?
>>701433258
>be me
>laugh at the question
>done mathematics for years
Rules of statistics:
For a (given that) statement the following equation must be used:
P(A|B)=P(AnB)/P(B)
Prob of A and B occurring is impossible so in this instance as both variables are independent you would do 50%/50%
Answer=25%
Or 1/4
Give me a challenge OP
>>701445322
Yeah, and he is laughing, because you fell for it.
"at least one" = position independent
stop using conditional probability, one flip does not influence the probability of the next flip so HT and TH are the same event.
one H one T = 1/2.
two H = 1/2.
I'm here for you anon. Don't fall for it.
>>701445501
not if you know that one of them will always be H
>>701444827
It's a 50% Chance one lands heads with two coins (4 possibilities), which is a 25% both will land heads.
With one coin always landing heads, it eliminates one possibility (TT). Making it a 66% one will land heads. Which is a 43.5% Chance both will land heads.
>>701445322
We aren't looking at the probability of the entire equation. We are looking at the probability that two individual coins will land heads. Because we've decided that one always has to land on heads thus modifying the equation.
The only options per coin are
H (1/3rd)
H (1/3rd)
T (1/3rd)
and
T (1/3rd)
H (1/3rd)
H(1/3rd)
Summing it up to a 66% Chance that a coin will land heads.
>>701433258
Don't look like regular coins to me
>>701445497
the answer is 1/3 i agree, but the question is still silly, people dont understand it the way its supposed to be understood, its not clear enough.
People here dont know that its a hypothetical math question, they think of it in the way that they flip 1 coin and its heads and then they are asked what are the odds of the other one being heads.
>>701435618
am i supposed to not see th eball cause I did
>>701445639
It's a good way of showing that one tail and one head is twice as common as two heads. It could've been
2/3=== TH
1/3=== HH
>>701445735
Still the right answer.
>>701445639
Thank you.
I love these threads because everyone overcomplicates everything.
Possible rolls:
HH
HT
TH
TT
"What is the probability that both landed heads given that at least one of them landed heads?"
This tells us only that TT is not a possible roll. That means there are still 3 possible rolls:
HH
HT
TH
Thus, HH has a 33% chance of occurring.
Why is 50% wrong? 50% assumes that since HT and TH are physically equivalent, they are also mathematically equivalent. This is not true. Mathematically, they are distinct events, each having a 33% chance of occurring.
>>701433258
1/3
>>701445735
And for the uneducated b/tards just because OP said "given that" doesn't mean that it's the same statistic as flipping the coin one time as one has already been down. It is statistically less likely to be the same face for the second time in a row therefore the rule still applies
>>701445986
There's a 1/3rd chance for the first coin to roll a T and the second coin to roll an H
There's a 1/3rd chance for the first coin to roll an H and the second coin to roll a T
There's a 1/3rd chance for the first coin to roll an H and the second coin to roll an H
Isn't that 2/3rds chance per coin to roll an H?
>>701445808
I suggest you sleep on this problem or play with coins
50/49.9735%
>.03481% land on edge
>>701442708
Great argument. you've convinced me.
>>701443021
>OP clearly states one coin will always land on heads
>will always
No it doesn't, you faggot. It says 2 coins were flipped and at least one landed heads. There is a difference.
>>701443352
How can you be this dumb. Your own pic proves you incorrect. If the FIRST coin landed heads, you can't have TH, you can only have
HH and HT
and the answer to that question is 1/3
The bottom half of your pic leaves TH out for some unknown reason. You have given the opposite answer to each question.
I can only assume that you are trolling at this point, as nobody could be this ignorant of their own errors/stupidity.
So I will ignore your posts from now on. For anyone still not sure about the answer to OP question,
Pic Related: Answer is 1/3
>>701445639
>>701445759
you dont know which of the coins is the forced heads, hence HT and TH are 2 different options.
>>701436473
Its not a logic question but a perception quest.
Are you asking the probability after the first coin flip or before both coin flips?
Basically, it's a poorly worded question open to interpretation to incite arguments.
>>701435310
If I remember correctly, that's where the optic nerve joins the something or other...
>>701445861
If you already know one of them will always be landing heads, then you are looking at just one flip, not two.
>>701443399
/thread
I think this is actually right..
>>701445986
>HT
>TH
lol
>>701446203
No. TT still exists, we're just ignoring it per "given that one of them landed heads."
>>701445986
They are only mathematically equivalent because you are using conditional probability. They are distinct events, when they happen seperately. If I flip two coins, which is the point of this ambiguous question (to use seperate, conditional or independent prob), they are not mathematically distinct events, and you are a sucker for saying so.
>>701446219
BOTH LANDED, you fucking moron, and one of them landed Heads.
What are the odds that both of them are heads, given that ONE ALREADY LANDED HEADS?
You gotta be joking at this point.
>>701443352
>> probability of two heads = 0.25
>> probability of two heads given -AT LEAST- one head: 0.5 (probability of a coin flip)
But that's wrong, you fucking retard.
probability of two heads = 0.25
probability of at least 1 heads = 0.75
probability of two heads given -AT LEAST- one head = (0.25) / (0.75) = 0.33
1/3
>they make HT and TH separate events, meaning there is a difference between the "first head second tails" and "first tails second head"
They are separate, distinct and equally probable outcomes. If you think otherwise, you're either retarded or trolling.
Using your logic:
penny = heads and quarter = tails
is the same as
penny = tails and quarter = heads
Clearly this is incorrect, and so are you.
1/3
>>701446412
I didn't say that the coin flips are distinct events. I said that HT and TH are distinct outcomes.
>>701446205
I suggest you do the same.
>>701443399
Correct.
>>701433258
>0%
There are no heads on euros
>>701446704
I feel like you arent gonna get it, go look it up on the internet or something, its basic probability, or just read the thread, it has been explained more than once here.
>>701444299
>I kinda kinda kinda see where you're coming from with how there's no real life equivalent
We're talking on skype and I flip 2 coins. i tell you that at least 1 of them landed heads, now you work out the probability that they are both heads.
There you go, Real life, no magic required.
1/3
Jesus H. Christ. Alright, all you fucking 50% morons, imagine it this way:
>you have 2 coins, a quarter and a nickel
>you throw them up in the air and close your eyes
>you ask your anon friend, "is at least one of them heads?"
>anon friend says yes
>so, either the quarter is a head and the nickel is a tail
>or the nickel is a head and the quarter is a tail
>or they're both heads
1 out of 3 is 33% you fucking idiots
>>701446356
no its not
>>701446704
The word "already" is not in the original image.
>What is the probability that both landed heads given that one landed heads?
>both landed
>one landed
Same tense. This implies to me that the flips take place simultaneously. There are four possible outcomes. We ignore one. There are now three possible outcomes.
>>701444182
>at least one
could be either HH, HT or TH
1/3
>>701433258
This is very simple but again this is 4chan so basically even if i were to go into detail on how and why we can answer this id still just be called a faggot.
>>701447109
OP never sayd that it needs 2 people or that you dont know which of the coins lands heads, hence my point about the question being misleading.
>>701433258
If anyone honestly believes the answer is anything other than 50% you should really kill yourselves to prevent further autistic genes being inherited.
read the fucking question.
>>701444664
>Well the people here dont know that its a hypothetical math problem
What?
>>701447093
>basic probability
>flips two coins
>one landed heads
>other is unknown
>the odds of both landing heads isn't 1/2
>logic
>>701447204
except the fucking question isn't asking you the probabilty of a specific outcome, i.e; HT
it's asking you the probability of the "other coin" landing on heads. 50%
>>701447269
"oh noes, someone knows math and i dont like it, please kill yourself so life will be easier for me and my children who also are bad at math."
Thanks for your contribution, made me giggle like a litte girl.
>>701447258
What are you talking about? All it says is "at least one of them landed heads." Obviously you don't know which one it is. It's "one of them."
>>701444406
>a coin is twice as likely to land heads
What flavor of retard are you?
>>701433258
This question is dilibrately confusing. The coin that is guranteed to land on heads is irelevant so the question is "what is the likely hood that one coin will lanf on heads. Oh yeah we also have another coin that has already landed on heads too."
>>701447313
just look at the fucking thread, count how many say its 50%
How many of us would say 50% if this question was never asked before and none of us knew anything about probability.
>>701444406
No, dumbass. TT is still an outcome, we're just ignoring it.
>>701447463
you are legitimately autistic
>thinks he's good at math
>gets a simple as fuck question wrong
Two US coins equal 30 cents and one of them isn't a nickel. What are the coins.
>can't be done according to /b/tard maths
>>701447666
But TT can't happen, so it's not an outcome. Which means 66%.
>>701438968
answer is 50%
you're taking the coin flip with two different guaranteed heads as a single event. When it would actually be two
>coin 1 is guaranteed heads: (HT:50%) (HH:50%)
>coin 2 is guaranteed heads: (TH:50%) (HH:50%)
which makes the probability of the desired result (HH):
(50%X50%)+(50%X50)=50%
>>701433258
If the first is heads, then the probability that the second is heads is 50%. But if all we know is that one of the two is heads, the probability that the other is also heads is 1/3.
>>701447478
PEOPLE DONT KNOW THAT FFS
>>701444802
>It's either HH or HT.
or TH
Do you understand that when you flip 2 coins, you are TWICE as likely to get a heads/tails result as you are to get a heads/heads result?
HH = 1/4
HT or TH = 1/2
TT = 1/4
At least one landed heads means TT is ruled out.
So now you have
HH = 1/3
HT/TH = 2/3
That's how the answer is 1/3.
mfw retards don't understand the difference between HT and TH
>>701447574
basically this, i really don't understand how these autismos can't grasp it
If anyone actually doubts that the answer's 1/3 you can always try a few coin tosses. It won't take that many to show that it's less that 50%
>>701444827
>what are the odds of the one being heads as well?
Different question to OP.
>>701438572
But that's the answer, anon.
>>701435173
You are adding a possability though. Our question does not account for order. Ht TH are the same event. Im not adding them together. They were divided by you and you alone.
>>701433258
33%
>>701447849
Yeah but its a 66% chance PER COIN to land heads. right?
>>701433258
100%,
>just tested haha
>>701443352
This is what happens when someone naturally bad at maths goes through a maths degree. It's like the knowledge is there but none of the intelligence.
If you've thought about it this much and you can't understand that the answer is 1/3 then there's no saving you.
>>701445639
>One of them will ALWAYS land heads.
>will always
>actually at least one coin already landed heads by chance
i see where you're making your error.
1/3
>Why are there three outcomes
If you flip 2 coins, there are 4 equally probable outcomes
HH
HT
TH
TT
If at least one coin landed heads, TT is the only outcome no longer possible, leaving three remaining outcomes, each of which is equally likely
HH = 1/3
Ht = 1/3
TH = 1/3
1/3
understand now?
Guys, just Google "conditional probability coin". This is a textbook example. Its solution is available in every statistics book.
It's 1/3 BTW.
>>701438572
>oh shit someone doesnt agree with me
>better tell them the kill themselves rather than show them why they are wrong
YOU are what is wrong with humanity, grow up.
To all 1/3 fags. Why does your autistic answer to this one doesn't follow the same logic anymore, all of sudden?
This is not more a question of probability or whatever mathematical concept you want to take. It is a question of who makes the most beautiful post.
How fucking stupid are you people? It's clearly 26%. Do the math, retards.
>>701445735
>Prob of A and B occurring is impossible
What are A and B here?
Here is my correct solution
A = "both coins are heads" {(H,H}
B = "at least one coin is heads" {(HH), (HT), (TH)}
P(A|B) = P(A∩B)/(P(B)) = (1/4)/(3/4) = 1/3
>>701447802
Of course it can happen. We're just ignoring outcomes in which it does.
>what are the chances of flipping heads
>50%
???????????????????????????????
???????????????????????????????
>what are chances of flipping heads BLAHBLAHBLAH
>50%
???????????????????
??????????????????????????????????????????????
>>701437075
God I hate python
>>701448471
Thank you
No its not. Your possibke answers are one heads one tails, two tails, two heads. The events you describe as HT and TH describe only one event not two. Youve made a mistake in defining the same event as two seprate ones.
>>701445759
>stop using conditional probability,
>for a conditional probability question
Sure thing, m8
Pic Related: 1/3
>>701448387
maybe its because there are 3 coins instead of 2?
in that case its
HHH
HHT
HTH
THH, So it should be 25%, this seems like a fun thing to test.
Coin A- Heads
Coin B- Heads
Coin A- Tails
Coin B- Tails
Coin A- Heads
Coin B- Tails
Coin A- Tails
Coin B- Heads
>>701448231
the fucking question isn't asking for one specific condition.
"what's the probability that the coin sequence is HT, given that at least one of them landed heads?"
HT
HH
TH
then it would absolutely be 1/3.
the question is asking you the probability both coins landed heads, irrelevant of the sequence, giving you two options
HH
TH/HT
it's 50, end of story.
>>701437743
Trials with one or more heads should be same as trials run fuckin idiot
>>701447175
This is probably the best way to explain it
>>701433258
Probably 0%, because i'm poor
>>701448387
Possible outcomes:
HHH
HHT
HTH
THH
HTT
THT
TTH
TTT
8 outcomes. We eliminate TTT, TTH, THT, HTT per "at least two of them landed heads."
This leaves:
HHH
HHT
HTH
THH
4 outcomes. 1 desirable outcome. 1/4 = 0.25 = 25%
>>701448990
best reply so far
>>701433724
>>701433800
It's not 50 percent fucking retards. It all falls on physics and the speed that it rotates and moves. You can't know what the percentage is until you can figure out a way to calculate how fast it is moving and spinning. Fags
>>701448736
The problem is that out of your three possible answers two of them are the same. And alaways have been. There were only three options. Two bjs, one bj one other, two other.
>>701446412
>They are only mathematically equivalent because you are using conditional probability.
Holy FUCK, you are retarded.
Take two different coins. Let's say, a penny, and a quarter. Each coin has a 50% chance of landing either heads or tails. You flip both coins. What are the possible outcomes? Well, let's see:
penny = heads & quarter = heads
penny = heads & quarter = tails
penny = tails & quarter = heads
penny = tails & quarter = tails
4 possible outcomes. Each of them equally likely to occur (25% or 1/4)
Now, surely we can all see how the results,
penny = heads & quarter = tails
and
penny = tails & quarter = heads
are different, right? Surely you can see how these are two distinct, separate and equally probable outcomes, yes?
Great, let's continue. Now, it DOES NOT MATTER if you are using two identical coins. HT & TH are two distinct results, and the probability of at least one of them occuring is TWICE the probability of a HH or TT outcome. Remember HT(1/4) + TH(1/4) = 1/2.
So, since we know that TT can't be the result in the OP question, it is discarded, and we are left with the possible outcomes:
HH (1/4)
HT (1/4)
TH (1/4)
Three equally probable outcomes containing at least one heads, hence the answer = 1/3
>>701447482
25% Chance Coin can land tails tails
25% Chance coin can land heads tails
25% Chance coin can land tails heads
25% Chance coin can land heads heads
You are FORCING one coin to land heads, which FORCES the outcome to not be TT
Means
33% Chance to land heads tails
33% Chance to land tails heads
33% Chance to land heads heads
BUT, what most people aren't getting is that by FORCING the outcome not to be negative, you're also FORCING the equation to entirely shift in a different direction.
Count the coin faces
4 Heads, 2 Tails, that means that by the very action of dismissing the TT result (2 additional tails). You've completely unbalanced the equation. Instead of it being a 50% chance for the coins to land on heads, each coin has a 66% chance to land on heads.
So its 43.5%, the math is sound.
>>701437075
Your equation accidentally is counting TT flips.
>>701448794
someone prove my logic wrong, i'm waiting.
>>701449147
He said that in response to my comment saying almost exactly the same thing as you. Good luck anon lol
>>701448794
Change the first question to:
"what's the probability that the coin sequence is HH, given that at least one of them landed heads?"
then it would absolutely be 1/3.
>>701449079
For the purpose of this arguement we assume that the coin has exactly a 50% chance to land on either side and lands in totally random way.
>>701446704
>What are the odds that both of them are heads, given that ONE ALREADY LANDED HEADS?
1/3
3 ways to have at least one heads for a 2 coin flip
coin1 = heads, coin2 = heads
or
coin1 = heads, coin2 = tails
or
coin1 = tails, coin2 = heads
So 1/3 for heads, heads
>>701449244
It's a 66% chance per coin that each is heads in your equation. Which doesn't exactly equal 50%, but it's not 1/3rd either.
>>701449209
4 heads?
>what flavor of retard are you?
>>701433258
basic s2 shit (a levels)
>>701448778
>>701448387
i actually tested it, i got 2 heads and a tails 11 times before i got the first 3 heads, i ignored all the results with more than 1 tails ofc.
Certainly its less than 50% yes?
>>701449328
never breed.
>>701433258
euros dont have heads
>>701447175
Good simple explanation, anon.
Thanks. Clearly the 50% faggots will ignore your clear and concise post.
>you have 2 coins, a quarter and a nickel
>you throw them up in the air and close your eyes
>you ask your anon friend, "is at least one of them heads?"
>anon friend says yes
>so, either the quarter is a head and the nickel is a tail
>or the nickel is a head and the quarter is a tail
>or they're both heads
1 out of 3 is 33% you fucking idiots
>It's this thread again
The answer is 50%.
>One coin will ALWAYS roll heads
>The chance of that coin rolling tails is 0 percent
>The chance of the opposite coin rolling either heads or tails is 50/50
The answer is 50%.
>>701433258
HOL UP /B/
U GOT 4 DEM BITCH MOODS AIGHT
SHE GIVES YOU
HEADZ, HEADZ
HEADZ, ASS
ASS, HEADZ
ASS, ASS
WE GETTIN HEAD 4 TYMES, AND ASS 4 TYMES
DEN YO BITCH BE LIKE "NAW NIGGUH, YOU CAN'T HAVE MY ASS TWICE IN A NIGH" SO YOU LIKE AIGHT.
WE GOT
HEADZ, HEADZ
HEADZ, ASS
ASS, HEADZ
SO 4 HEADZ AND 2 ASS, SO 66% OF THE TIME WE GET HEADZ AND 33% OF THE TIME WE GET SUM ASS.
SO WHAT, 66%*66% CHANCE TO GET DOUBLE HEADZ?
43% NIGGUH?
PIMPIN AINT EZ YO
>>701447448
>except the fucking question isn't asking you the probabilty of a specific outcome
Yes it is.
>What is the probability that both landed heads (HH) given that at least one landed heads (HH, HT, TH)?
1/3
>it's asking you the probability of the "other coin" landing on heads
haha, no it's not you dumbass. Read it.
>>701448778
>>701449054
>>701449528
If the idiot fails to understand once, you try it again.
How about now?
>>701449807
this.
the sequence order is NEVER mentioned in this question, which is the fundamental error you neckbeards are obsessing over
>sequence irrelevant
>>701449807
you mean you have been in these threads before and you still think the answer is 50%
kys, infact all you fags who insist its 50% despite it being shown time and time again that its 1/3, just kys asap tbh.
>>701449906
you trolling or completely autistic?
>>701449209
>You are FORCING one coin to land heads
No, retard. No coin was forced to land heads. 2 coins were flipped and at least one of the 2 landed heads by chance. There is a difference.
>what most people aren't getting is that by FORCING the outcome
It wasn't forced, dumbass. Your reading comprehension and logic skills need some work.
By your retarded logic, if I flip 10 coins and at least 3 of them landed heads, then they were FORCED to land heads. Doesn't work like that, son.
2 coins were flipped
At least 1 landed heads
Could be HH, HT or TH
1/3
>>701450112
It is not 33%, it's impossible for the one coin to roll tails. Therefore it is impossible for there to be three outcomes. Therefore it's 50% chance, shitlord.
T/H
H/H
Only possible outcomes.
>>701447574
>The coin that is guranteed to land on heads is irelevant
Which coin?
>>701449916
1/n+1?
just a guess tho, im not a math fag.
>>701450407
the coin guaranteed to land on heads obviously, you thick cunt
>>701447819
>lists HH twice
Damn, you must be trolling anon.
Flip a penny and a quarter. At least 1 of them landed heads, so you could have
penny = heads, quarter = tails
or
penny = tails, quarter = heads
or
both heads
3 equally probable outcomes
both heads is 1 of the 3
1/3
>>701450407
it doesnt fucking matter which one lands head the question is if the other will
>>701450362
Except the 1 head and 1 tail scenario is twice as likely as the 2 heads scenario. Why don't you give it a try with some real coins.
"I could either win the lottery or not win the lottery, therefore there is a 50% chance I will win the lottery" <---- your logic
in the end of the day the question doesn't care whether the coins rolled HT or TH, it only cares about HH or none
1 or 0
it's 50%
you may know direct math but lack basic reading comprehension
bunch of retards, i'm out
>>701448134
No.
>>701449861
Wait wait, that makes sense.
We got 4 results
Head, Head
Head, Tails
Tails, Head
Tails, Tails
4 Heads, 4 Tails. So for each coin it's a 50% chance for each to occur. 50% * 50% = 25% for both to be heads, or 25% for both to be tails.
So we remove TT from the equation
Head, Head
Head, Tails
Tails, Head
4 Heads (still), 2 Tails. Which is now 66% chance to get heads per coin, but a 33% chance to get tails per coin. So the probability to get heads is now 66% * 66%,
or 43.5%
Why does that not work?
>>701448033
>You are adding a possability though
I added nothing. I eliminated TT based on the condition of at least 1 coin landing heads.
>Ht TH are the same event.
No they are not the same event.
>>701450856
To you and all that argue like this.
See >>701450108
This implementation doesn't care for HT or TH, they are both treated equally and you still get 1/3.
>>701450776
It would be twice as likely if you didn't have one coin that was guaranteed to roll heads.
Let's do a simple test
Take two coins
Place one heads up
flip the other
What's the chance the coin you flipped is also heads up?
FIFTY.
PERCENT.
The chance that both coins will land on heads is FIFTY percent because one coin will ALWAYS land on heads.
What don't you understand about this?
>>701448387
All 8 outcomes for a 3 coin flip
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
4 of them contain at least 2 heads
1 of those 4 is all heads
So 1/4
Answer to OP is 1/3, using same solution
>>701449126
>two of them are the same
No, they are not. Just because they LOOK the same to retards, does not mean that they are not 2 distinct, separate and equally probable outcomes.
Here I drew you a Venn diagram.
1/3
If I do this right...
Probability that one is heads is 0.5%
Probability that other is heads is 0.5%
So probability of both heads is
0.5 x 0.5 = 0.25%
Maybe I didn't learn anything in math class but that is my best attempt
>>701451608
0.25% is 1 in 400 m8.
>>701449916
you're making the retarded assumption that the first n-1 coins landed heads, in which case the nth coin has a 1/2 probability to land heads
What you are missing is that the nth coin could be in any position, meaning there are 2^n - 1 ways to get at least n-1 heads coins.
Answer to OP is 1/3
>>701451608
>If I do this right...
>Probability that one is heads is 0.5%
>Probability that other is heads is 0.5%
You're almost right
Probability that one is heads is 1
probability that the other is heads is 0.5
>>701451741
I meant 0.25 as 25% sorry
>>701451916
Yeah I get it now thanks
>>701450108
>counting only results with at least one face
re-write your program to calculate the probability two faces show when one face will ALWAYS show
>>701450220
Which coin is the "other coin", you simpleton.
there are 3 ways to get at least one heads
HH, HT, TH
HH is 1 of those 3
1/3
>>701451309
>It would be twice as likely if you didn't have one coin that was guaranteed to roll heads.
Neither coin is guaranteed. You know at least one has landed heads, you don't know which one. That's the entire premise of the question.
>Let's do a simple test
>Take two coins
>Place one heads up
>flip the other
>What's the chance the coin you flipped is also heads up?
>FIFTY.
>PERCENT.
>The chance that both coins will land on heads is FIFTY percent because one coin will ALWAYS land on heads.
>What don't you understand about this?
Why are you inventing a test that's different to the question? Why not just test what the question is asking? Try it for yourself, friend. Get two coins out of your wallet, flip them together 1000 times, discard the instances where two tails landed, calculate the percentage of instances remaining which were HH, discover you're a fucking idiot.
1
>>701450362
No, it's impossible for BOTH coins to roll tails given that at least 1 rolled heads.
Still 3 outcomes possible
HH
HT
TH
1/3
>>701438065
Underrated post
>>701452036
>re-write your program to calculate the probability two faces show when one face will ALWAYS show
That's what's happening.
>>701451349
Ok, try this again, now with a slightly bigger number.
If your answer still isn't 50%, then add a few hundred thousand more coins, which all landed heads, except one, and try again.
It's basically if you flipped two coins, picked one at random and turned it so that it was heads up. Then look at the other one. What is the probability they are both heads now?... .5
It's not a permutation problem, it's a P(A|B).
IT'S A TROLL QUESTION PEOPLE!
>>701450525
And which of the 2 coins is that?
Unless you can specify which coin it is, then EITHER coin could be tails, just not both, which gives 3 equally likely outcomes
heads, heads
or
heads, tails
or
tails, heads
1/3
>>701452050
you are seriously fucking retarded
1 coin will always land heads
CoinA or CoinB
lets say CoinA lands heads, CoinB has a 50% chance of landing heads
lets say CoinB lands heads, CoinA has a 50% chance of landing heads
utter. fucking. morons.
>>701433258
0%
/thread
>>701451041
Fuck off samefag
People saying 50% are trolls, could we stop with this thread?
And if they re not actually trolling, just play the game yourself and count.
Also, you lost.
>>701451912
>you're making the retarded assumption that the first n-1 coins landed heads
That's the whole premise of the problem, you fucking pile of hot diarrhea.
>>701452187
coin#1: random 0 or 1
coin#2: as above
no it's not.
change
coin#1: to 1
coin#2: random 0 or 1
do it Anon, if it returns as 66% i'll apologise and accept it's 1/3
i'm not into programming so unless you can guarantee one of the coins will land heads, which you haven't, the result is invalid
>>701433258
>1%
>>701452217
holy FUCK you are retarded.
Read this >>701451912
Do you understand that there are MANY ways to get at least n-1 heads for n flips?
Let's try explaining it to you with 4 coins.
4 coins are flipped. At least 3 landed heads, What is the probability that all 4 landed heads.
Well, for a 4 coin flip, there are 2^4 = 16 possible outcomes:
HHHH
HHHT
HHTH
HHTT
HTHH
HTHT
HTTH
HTTT
THHH
THHT
THTH
THTT
TTHH
TTHT
TTTH
TTTT
Now how many of those contain at least 3 heads? Count them and the answer is 5
how many of those 5 contain all heads> Answer is 1
so 1 in 5
1/5
Can you understand how you are not calculating the probability of the last (nth) coin landing heads?
You are claculating the probability that all coins landed heads given that at least 3 of them did
5 different and equally likely ways to get at least 3 heads.
1 of those is all heads (HHHH)
Answer to OP question is 1/3
>>701452807
That's not what the instructions say.
I re-wrote the comments to directly quote the instructions. I don't know how to make it any easier to understand.
>>701452731
Imagine this, a stranger flips two coins, then quickly covers one with his hand.
The uncovered coin is heads.. what is the chance the covered coin will be a heads as well? It's a single coin, so 50/50.
Answer = 50%.
A coin was flipped 50 times and landed on heads all of the times. What are the odds that it will land on heads again?
>>701452807
You misread the question, friendo. The question stated that "at least one of them is heads". It doesn't specify which one.
>>701452316
>1 coin will always land heads
ERRRRRRR Incorerct. Would you like to try again.
Protip: 2 regular coins were flipped and at least one landed heads
coinA = heads, coinB = tails
or
coinA = tails, coinB = heads
or
both coins = heads
1/3
moron
>>701453121
bolton wanderers?
>>701453056
This is a different situation because you know which coin is heads which eliminates 2 possibilities rather than one.
>>701433258
>>701452794
>>you're making the retarded assumption that the first n-1 coins landed heads
>That's the whole premise of the problem, you fucking pile of hot diarrhea.
You see this is how you are retarded. you think that there is only 1 way to get at least n-1 heads.
Let's' stick with 2 coins.
You flip 2 coins. How many ways can you get at least 1 heads?
>>701453056
too bad the actual answer is 1/3, go fucking test it if you dont believe and dot get lazy and make the sample size like 10, spend the rest of the day flipping coins and see where it takes you.
>>701453121
Buenos Aires?
>>701453006
>Do you understand that there are MANY ways to get at least n-1 heads for n flips?
THE PROBLEM STATES THAT AT LEAST n-1 LANDED HEADS, YOU FUCKING MORON!
Holy fuck, how can someone be this retarded and still be able to use a computer?
>>701453299
Shut up, this thread is always lots of fun for some reason.
>>701453380
>>701453056
That's a different question. in OP question you have no way of knowing which coin is heads.
3 possibilities
HH
HT
TH
1/3
>>701452155
>Neither coin is guaranteed.
Then it's 25% chance because both coins can roll tails.
Either it's 50% or it's 25%. 33% is not possible.
I just did your little test, did it out of ten times, twice, discarded the TTs.
6 HH
4HT
5 TT
Second run
5 HH
5TH
6TT
The chance is fucking 50 percent.
>>701453335
>You see this is how you are retarded. you think that there is only 1 way to get at least n-1 heads.
THE PROBLEM SAYS IT LANDED HEADS ALREADY YOU FUCKING PILE OF GARBAGE!
>>701453335
3
TH
HT
HH
go fucking test it you nigger, flip the coins at the same time and ignore the TT results, then see how many of the flips are HH, makes the sample size 1000 and i promise that you will see the truth.
>>701453121
The sixth sick sheik's sixth sheep's sick?
