One hundred identical coins, each with probability `p ,` of showing up heads are tossed once. If `0<p<1` and the probability of heads showing on 50 co

Question

One hundred identical coins, each with probability p, of showing up heads are tossed once. If `0 A. 1/2 B. 51/101 C. 49/101 D. none of these Select the correct answer from above options

Answer 1

Correct Answer - B Let X be the number of coins showing heads. Then, X is a binomial variate with parameters, n = 100 n and p. P ( X = 50 ) = P ( X = 51 ) P ⇒ . 100 C 50 p 50 ( 1 − p ) 50 = . 100 C 51 ( 1 − p ) 49 ⇒ ⇒ 100 ǃ 50 ǃ × 50 ǃ × ⇒ 51 ǃ 49 ǃ 100 ǃ = p 1 − p ⇒ 51 50 = p 1 − p = 51 101 ⇒ .