Question

A fair coin is tossed a fixed number of times. If the probability of getting seven heads is equal to that of getting nine heads, the probability of getting two heads, is A. `15//2^8` B. `2//15` C. `15//2^13` D. none of these Select the correct answer from above options

Answer 1

Correct Answer - C 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)`.