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Probability PS

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Re: Probability PS

by 4meonly » Sat Sep 27, 2008 10:13 am
gmatstud25 wrote:what is the probability that a coin lands tail on exactly the 4 attempt in a total of 6 attempts?
The probability of getting exactly k results out of n flips is:
nCk/2^n

answer 15/64?
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Re: Probability PS

by Stuart@KaplanGMAT » Sat Sep 27, 2008 11:19 am
4meonly wrote:
gmatstud25 wrote:what is the probability that a coin lands tail on exactly the 4 attempt in a total of 6 attempts?
The probability of getting exactly k results out of n flips is:
nCk/2^n

answer 15/64?
Perfect!

To elaborate a bit:

6C4/2^6 = (6!/4!2!)/64 = (6*5*4*3*2/4*3*2*2)/64 = 15/64
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Probability PS

by gmatstud25 » Sat Sep 27, 2008 1:31 pm
The question is "what is the probability of getting tails on the 4th attempt and not getting exactly 4 tails in 6 attempts"
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by csandeepreddy » Sat Sep 27, 2008 6:20 pm
I think the probability should still be 1/2.
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by cramya » Sat Sep 27, 2008 7:03 pm
Hi Stuart,
At your earliest convenience could you please look in to the coin flip strategy post and let us know how to do it.

We are not sure on how to use the pascals triangle approach there. Its one post above this one.

Thanks!
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Re: Probability PS

by Stuart@KaplanGMAT » Sat Sep 27, 2008 8:53 pm
gmatstud25 wrote:The question is "what is the probability of getting tails on the 4th attempt and not getting exactly 4 tails in 6 attempts"
I just assumed that the question had been misquoted.

If the question is actually "what is the probability of getting tails on the 4th attempt out of 6 attempts", then the answer would be 1/2, since the probability of getting tails on any flip is 1/2, assuming it's a "fair coin".

I'm pretty sure the question should have been "If a fair coin is flipped 6 times, what's the probability of getting tails on exactly 4 of the 6 flips".
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by Stuart@KaplanGMAT » Sat Sep 27, 2008 8:54 pm
cramya wrote:Hi Stuart,
At your earliest convenience could you please look in to the coin flip strategy post and let us know how to do it.

We are not sure on how to use the pascals triangle approach there. Its one post above this one.

Thanks!
I'm not sure which post you mean, sorry.
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by cramya » Sat Sep 27, 2008 9:25 pm
I should have been more specific.

This is the post I am referring to
https://www.beatthegmat.com/coin-flip-st ... 19517.html

Thanks!
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by sumithshah » Tue Sep 30, 2008 5:34 am
The coin flip shortcut ( which uses Combinations ) is a specific case of a Generalization called Binomial theorem.

BT says : If probability of success of event is X and probability of failure is Y and if we want N successes out of M tries then the resultant probability is

mCn * (x)^n * (y)^(m-n)
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