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Question

One hundred identical coins each with a probability p of showing up heads are tossed once. If 0<p<1 and the probability of heads showing on 50 coins are equal to that of heads showing on 51 coins, then the value of p is


A

12

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B

49101

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C

50101

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D

51101

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Solution

The correct option is D

51101


Explanation for the correct option

Let X be the number of coins that show heads

Then X~B(100,p)

On the basis of the given information

P(X=50)=P(X=51)C50100p50q50=C51100p51q49Crnprqn-r

On solving, we get:

5150=pq5150=p1-p[p+q=1]p=51101

Hence, the correct answer is option (D).


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