A fair coin is tossed a fixed number of times. If the probability of getting seven heads is equal to that of getting nine heads, the probability of getting two heads, is

A fair coin is tossed a fixed number of times. If the probability of getting seven heads is equal to that of getting nine heads, the probability of getting two heads, is

  1. A

    15/28

  2. B

    2/15

  3. C

    15/213

  4. D

    none of these

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    Solution:

    Let n be the total number of tosses and X be the number of times head occurs. Then, X is a binomial variate with parameters n and p = 1/2.

    Now,

    P(X=7)=P(X=9)

    nC712712n7=nC912912n9nC7=nC9n=16P(X=2)=16C212212162=15213

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