Let a die be rolled n times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is k 2 15 , then k is equal to

Step-by-step solution

Given that P (getting odd 7 times) = P (getting odd 9 times). This is the case of binomial distribution with n successes and probability of success = p = 3 6 and failure is q = 1 - p = 1 2 . We know that P X = k = C k n p k q n - k Now P X = 7 = P X = 9 ⇒ C 7 n 1 2 7 1 2 n - 7 = C 9 n 1 2 9 1 2 n - 9 ⇒ C 7 n = C 9 n ⇒ C n - 7 n = C 9 n ⇒   n   =   16 ⇒ P ( 2   times   even   ) = C 2 16 1 2 14 1 2 2 = 15 × 4 2 15 = 60 2 15 = k 2 15 ⇒ k = 60 Hence