A pair of fair dice is thrown 4 times. If getting the same number on both dice is considered as a success, then the probability of two successes are

Step-by-step solution

The probability of getting identical numbers on both dice in a single throw is p = 6 36 = 1 6 , with complementary probability q = 5 6 . With n = 4 independent trials and k = 2 successes required, the binomial probability is P(X=2) = C(4,2) ( 1 6 )^2 ( 5 6 )^2 . The binomial coefficient evaluates to C(4,2) = 4! 2!2! = 6 , so: P(X=2) = 6 1 36 25 36 = 150 1296 = 25 216 This corresponds to option A.