A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of a number of successes and hence find its mean.

Throwing doublet: {(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}

Total outcomes = 6×6 = 36

Let p = probability of success

So, q = 1 - p

Given, n = 4

The required binomial distribution is given by,

Let, X, be the random variable getting doublet, so,

20