Probability of a student reading in school and playing cricket

To solve this problem, we need to understand the definitions of probability and set theory.

Probability: Probability is the measure of the likelihood of an event occurring.

Set theory: Set theory is the branch of mathematics that deals with the study of sets, which are collections of objects.

In this problem, we are given two events:

A: A student reads in a school
B: A student plays cricket

We need to find the probability of the event A and B occurring together.

Intersection of two events

The intersection of two events is the set of elements that belong to both events.

In set theory, the intersection of two sets A and B is denoted by A ∩ B.

For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}.

Probability of intersection of two events

The probability of the intersection of two events A and B is denoted by P(A ∩ B).

P(A ∩ B) represents the probability that both A and B occur.

Formula:

P(A ∩ B) = P(A) * P(B|A)

where P(B|A) represents the probability of B occurring given that A has already occurred.

If A and B are independent events, then P(B|A) = P(B), and the formula reduces to:

P(A ∩ B) = P(A) * P(B)

Solution

In this problem, we are not given any information about the relationship between A and B.

Therefore, we cannot assume that they are independent events.

Since we do not have any information about the relationship between A and B, we cannot calculate the probability of their intersection.

Therefore, the correct answer is option C: P(A ∩ B) = 0.

This mathematical expression indicate the no. of common student who reads as well as play
therefore, there is no common student as per the question

hence, it equals to zero