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Coin Probability

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Coin Probability

by amsm25 » Mon May 07, 2012 12:45 am
The probability that a certain coin will fall heads up is 50%.What is the probability that it falls heads up on 3 of 6 tosses?

a)41/2^6
b)35/2^6
c)1/2^6
d)21/2^5
e)5/2^4

OA- E
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by mathbyvemuri » Mon May 07, 2012 1:07 am
It's a formula based problem.
"The probability of getting exactly k results out of n flips is: nCk/2^n"
6C3/2^6 = 20/2^6 = 5/2^4
Answer option "E"
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by Bill@VeritasPrep » Mon May 07, 2012 7:29 am
If we're looking for exactly 3 heads (and therefore exactly 3 tails), we can use our permutation with repeating elements formula: 6!/(3!3!) = 20. For any binomial event, the total number of possibilities is equal to 2^n where n is the number of events. 2^6=64, so the probability of exactly 3 heads is 20/64, or 5/16, which is 5/2^4.
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