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One hundred identical coins, each with p...

One hundred identical coins, each with probability `p ,` of showing up heads are tossed once. If `0

A

`1/2`

B

`49/101`

C

`50/101`

D

`51/101`

Text Solution

Verified by Experts

The correct Answer is:
D
Let X be number of coins showing heads. Let X be a biomial variate with parameters n=100 and p.
Since, P(X=50)=P(X=51)
`rArr overset(100)""C_(50)p^(50)(1-p)^(50)=overset(100)""C_(51)(p)^(51)(1-p)^(49)`
`rArr ((100)!)/((50)!(50)!).((51!)xx(49!))/(100!)=(p)/(1-p)rArr(p)/(1-p)=(51)/(50)`
`rArr " "p=(51)/(101)`
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