A die is tossed thrice. If event of getting an even number is a success, then the probability of getting at least 2 successes is

Step-by-step solution

Let X denotes the number of successes in 3 trials. Then, X is a binomial variate with n = 3 , p = 3 6 = 1 2 . Then, P ( X = r ) = C r 3 1 2 r ,   r = 0 ,   1 ,   2 ,   3 Therefore, the required probability of getting at least two successes is P ( X ≥ 2 ) = P ( X = 2 ) + P ( X = 3 ) = C 2 3 1 2 3 + C 3 3 1 2 3 = 3 × 1 2 3 + 1 2 3 = 1 2 3 × 4 = 1 2