Please explain:

99. A fair coin is tossed n times. If the probability of getting 7 heads is equal to the probability of getting 9 heads, then the value of n will be.
(a) 8           (b) 13

(c) 15         (d) None of these.

Tossing a fair coin n times is a binomial distribution with probability of success, p=12Pr successes=PX=r=Crn pr 1-pn-rGiven PX=7=PX=9C7n 127 1-12n-7=C9n 129 1-12n-9C7n 127 12n-7=C9n 129 12n-9C7n 12n-7+7=C9n  12n-9+9C7n 12n=C9n 12nC7n=C9nUsing Crn=Cn-rnC7n=Cn-9nComparing7=n-9n=16

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P(X=7) = P(X=9)
nC7 (1/2)7 (1/2)n-7nC9 (1/2)9 (1/2)n-9
thus, n=16
so according to your question, answer is option D! (none of these)

Hope this helps :)
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