SOLUTION: $n$ coins are simultaneously flipped. The probability that at most one of them shows tails is $\frac{3}{16}$. Find $n$.

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Question 1117200: $n$ coins are simultaneously flipped. The probability that at most one of them shows tails is $\frac{3}{16}$. Find $n$.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The probability of getting "r" tails when flipping "n" coins is

C%28n%2Cr%29%2F%282%5En%29

At most 1 tails means either 0 tails or 1 tails. So we have

C%28n%2C0%29%2F%282%5En%29%2BC%28n%2C1%29%2F%282%5En%29+=+3%2F16
1%2F%282%5En%29%2Bn%2F%282%5En%29+=+3%2F16
%28n%2B1%29%2F%282%5En%29+=+3%2F16
16%2A%28n%2B1%29+=+3%2A%282%5En%29

That equation can't be solved algebraically; but simple enumeration finds that n is 5:

16%2A%28n%2B1%29+=+16%2A6+=+96
3%2A%282%5En%29+=+3%2A%282%5E5%29+=+3%2A32+=+96