A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.

We know that the repeated tosses of a pair of dice are known as Bernouli trials.

Let the number of times of getting doublets in an experiment of throwing two dice simultaneously four times be x.

Thus, P(X = x) = nCxqn-xpx , where x = 0, 1, 2, …n

= 4Cx (5/6)4-x(1/6)x

= 4Cx (54-x/66)

Hence, Probability of getting 2 successes = P(X = 2)

= 4C2(54-2/64)