Binomial Distribution

A doublet is obtained when both dice show the same number, such as (1,1), (2,2), ..., (6,6).
There are 6 such outcomes out of a total of outcomes when a pair of dice is thrown once.
So, the probability of getting a doublet in one trial is .
Now, the dice are thrown twice.
Let be the number of doublets obtained in 2 independent trials.
Then follows a Binomial distribution with , .
The expectation .
So, the expected number of doublets is .