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.

Explanation

To solve the problem step by step, we will first determine the probability of getting a doublet when a pair of dice is thrown, then find the probability distribution of the number of successes when the dice are thrown four times, and finally calculate the mean of the distribution.

### Step 1: Determine the probability of getting a doublet
A doublet occurs when both dice show the same number. The possible doublets when rolling two dice are:
- (1, 1)
- (2, 2)
- (3, 3)
- (4, 4)
...