Question

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

Answer 1

Since each trial in this problem is Bernoulli trials, therefore we can apply binomial distribution as

 Now probability distribution table is

X or xi	0	1	2	3	4
P(X) or pi	625/1296	500/1296	150/1296	20/1296	1/1296

Now mean E(X) = ∑p_ix_i = 0 x 625/1296 + 1 x 500/1296 + 2 x 150/1296 + 3 x 20/1296 + 4 x 1/1296

= (500 + 300 + 60 + 4)/1296 = 864/1296 = 2/3