A fair coin is tossed n times . If the probability of getting seven heads is equal to the probability of getting 9 heads , then the probability of getting two heads is

Options

A. `15//2^8`
B. `2//15`
C. `15//2^13`
D. none of these

Answer

C

Explanation

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`.
`P(X=7)=P(X=9)`
`rArr .^n C_7((1)/(2))^7((1)/(2))^n-7=.^nC_9((1)/(2))^9((1)/(2))^n-9rArr .^nC_7=.^nC_9rArr n=16`
`therefore P(X=2)=.^16C_2((1)/(3))^2((1)/(2))^16-2=(15)/(2^13)`.