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Question

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


A

12

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B

51101

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C

49101

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D

None of these

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Solution

The correct option is B

51101


Explanation for the correct option:

Given. Total coin is hundred.

The probability of the head showing on 50 coins are equal to that of the head shown on 51 coins

Applying binomial distribution for 100 trials using the formula Crn(p)r(q)n-r we get

100C50p50(1p)50=100C51p51(1p)49(1p)50=p511p50=p515151p=50p101p=51p=51101

Hence, the correct answer is option (B).


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