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

Explanation

To find the probability distribution of the number of successes when a pair of dice is thrown 4 times, and getting a doublet is considered a success, we can follow these steps:

### Step 1: Determine the Probability of Success (P) and Failure (Q)
When rolling a pair of dice, the total number of outcomes is \(6 \times 6 = 36\). A doublet occurs when both dice show the same number. The doublets possible are: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6), giving us a total of 6 doublets.

Thus, the probability of getting a doublet (success) is:
\[
P = \frac{6}{36} = \frac{1}{6}
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