NCERT Class 12-Mathematics: Chapter – 13 Probability Part 4 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Question 10:

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


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:

Thus the Probability Distribution of X

Variance of

Where μ is the mean of given by


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 .


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?


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






The correct answer is (D) .

From the given data .

This shows that . Thus