# NCERT Class 12-Mathematics: Chapter – 13 Probability Part 15 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 51**:

The probability distribution of a random variable is given as under:

where is a constant. Calculate

(i)

(ii)

(iii)

**Answer**:

Otherwise | |||||||

We know that,

(i) . So,

(ii) Also,

(iii)

**Question 52**:

A bag contains coins. It is known that *n* of these coins have a head on both sides whereas the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is determine the value of .

**Answer**:

Given, coin have head on both sides and coins are fair coins.

Let

Also,

**Question 53**:

Two cards are drawn successively without replacement from a well shuffled deck of cards. Find the mean and standard variation of the random variable where is the number of aces.

**Answer**:

Let denotes a random variable of number of aces.

Now,

We know that,

Also,