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Question

Suppose X follows a binomial distribution with parameters n and p, where 0<p<1. If P(X=r)P(X=n−r) is independent of n and r, then p is equal to

A
13
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B
12
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C
14
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D
None of these
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Solution

The correct option is D 12
P(X=r)P(X=nr)=nCrpr(1p)nrnCnrpnr(1p)r=(1p)n2rpn2r=(1p1)n2r
For (1p1)n2r to be independent of n and r,1p1=1
1p=1p=12.

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