SOLUTION: n coins are simultaneously flipped. The probability that at most one of them shows tails is 3/16. Find n.

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Question 394013: n coins are simultaneously flipped. The probability that at most one of them shows tails is 3/16. Find n.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The probability that at most one of n coins show tails is
nC0%2A%281%2F2%29%5En%2A%281%2F2%29%5E0+%2B+nC1%2A%281%2F2%29%5E%28n-1%29%2A%281%2F2%29%5E1
= %281%2F2%29%5En+%2B+n%281%2F2%29%5En
= %28n%2B1%29%281%2F2%29%5En.
Now the above sequence STRICTLY DECREASES as n INCREASES, because
%28n%2B1%29%2F2%5En+%3C+n%2F2%5E%28n-1%29+ for n+%3E+1.
Values for n =1,2,3,4,5 will not satisfy %28n%2B1%29%281%2F2%29%5En+=+3%2F16, but n = 6 will. Since the sequence %28n%2B1%29%281%2F2%29%5En is strictly decreasing, 6 is the only value of n that will satisfy the problem.
Therefore there were 6 coins.