**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

**Answer **: option (B)

**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