# NCERT Class 12-Mathematics: Chapter – 13 Probability Part 11 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**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.