# NCERT Class 12-Mathematics: Chapter – 13 Probability Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 10**:

Determine variance and standard deviation of the number of heads in three tosses of a coin.

**Answer**:

Let X denote the number of heads tossed. So, can take the values . When a coin is tossed three times, we get

Sample space

Thus the probability distribution of is:

Variance of

Where μ is the mean of given by

Now

From (1) , (2) and (3) , we get

Standard deviation

**Question 11**:

Refer to Example . Calculate the probability that the defective tube was produced on machine .

**Answer**:

Now, we have to find .

**Question 12**:

A car manufacturing factory has two plants, X and Y. Plant X manufactures of cars and plant Y manufactures of the cars at plant X and of the cars at plant Y are rated of standard quality. A car is chosen at random and is found to be of standard quality. What is the probability that it has come from plant X?

**Answer**:

Let be the event that the car is of standard quality. Let and be the events that the car is manufactured in plants X and Y, respectively. Now

Probability that a standard quality car is manufactured in plant

Probability that a standard quality car has come from plant

Hence the required probability is

## Objective Type Questions

### Choose the Correct Answer from the Given Four Options in Each of the Examples 13 to 17

**Question 13**:

Let A and B be two events. If is equal to

(A)

(B)

(C)

(D)

**Answer**:

The correct answer is (D) .

From the given data .

This shows that . Thus