# An unbiased coin is tossed n times. If the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then n=

Question : An unbiased coin is tossed n times. If the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then n=

(A) 7

(B) 14

(C) 16

(D) 19

Solution :

Let X denote the number of heads n in trials. Then X is a binomial variant with p = q = 1/2.

Therefore, $P( X= r) =nC_{r}\left( \dfrac{1}{2}\right) ^{n}$

now, P(X = 6) = P(X = 8)

$\Rightarrow nC_{6}\left( \dfrac{1}{2}\right) ^{n}=nC_{8}\left( \dfrac{1}{2}\right) ^{n}$ $\Rightarrow nC_{6}=nC_{8}$

therefore, n=14

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