# NCERT Class 12-Mathematics: Chapter –13 Probability Part 11

Get top class preparation for UGC Public-Administration right from your home: fully solved questions with step-by-step explanation- practice your way to success.

**Question 35:**

Find the probability distribution of the maximum of the two scores obtained when a die is thrown twice. Determine also the mean of the distribution.

**Answer:**

**Question 36:**

The random variable X can take only the values . Given that and that , find the value of .

**Answer:**

Since, and is , let at is

We get, the following distribution.

And

Also, given that

**Question 37:**

Find the variance of the distribution:

**Answer:**

**Question 38:**

A and B throw a pair of dice alternately. A wins the game if he gets a total of and B wins if she gets a total of . It A starts the game, find the probability of winning the game by A in third throw of the pair of dice.

**Answer:**

Let

And

Let is the probability, if A wins in a throw

And is the probability, if B wins in a throw

Required probability

**Question 39:**

Two dice are tossed. Find whether the following two events A and B are independent:

where denotes a typical sample point.

**Answer:**

We have,

So, A and B are not independent.