A fair coin is tossed `n` times. if the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then find the value of `ndot`

Options

A. 7
B. 14
C. 16
D. 19

Answer

B

Explanation

let X denotes the number of heads in heads in n trials . Then, X is a binomial variate with `p=q=1/2`
`therefore P(X=r) = ""^(n)C_(r)(1/2)^(n)`
`because P(X=6)=P(X=8)implies ""^(n)C_(6)(1/2)^(n)=""^(n)C_(8)(1/2)^(n)`
`implies ""^(n)C_(6)=""^(n)C_(8)implies n=14`