One hundred identical coins, each with probability `p ,` of showing up heads are tossed once. If `0

Options

A. `(1)/(2)`
B. `(49)/(101)`
C. `(50)/(101)`
D. `(51)/(101)`

Answer

D

Explanation

(d) Let X denots the number of coins showing heads up. Then, X is a biomial variate with n=100 and probability of success p.
We have, P(X=51)=P(X=50)`" "` [given]
`rArr " " ""^(100)C_(51)p^(51)q^(49)=""^(100)C_(50)p^(50)q^(50)`
`rArr " "(p)/(q)=(""^(100)C_(50))/(""^(100)C_(51))=(50)/(51)`
`rArr " "(p)/(1-p)=(51)/(50)" "` [q=1-p]
`rArr " " p=(51)/(101)`