What is the probability of intersection of two events?

The probability of intersection of two events is the probability that both events occur.

When two events A and B are considered, the probability of their intersection is denoted by P(A ∩ B). This is the probability that both A and B occur simultaneously. The formula for calculating the probability of intersection is:

P(A ∩ B) = P(A) x P(B|A)

where P(A) is the probability of event A occurring and P(B|A) is the conditional probability of event B occurring given that event A has occurred.

If the events A and B are independent, then the conditional probability P(B|A) is equal to the probability of event B occurring, i.e. P(B|A) = P(B). In this case, the formula simplifies to:

P(A ∩ B) = P(A) x P(B)

For example, if the probability of event A occurring is 0.4 and the probability of event B occurring is 0.3, and the events are independent, then the probability of their intersection is:

P(A ∩ B) = 0.4 x 0.3 = 0.12

If the events A and B are mutually exclusive, i.e. they cannot occur simultaneously, then the probability of their intersection is zero, i.e. P(A ∩ B) = 0. This is because if event A occurs, then event B cannot occur, and vice versa.

In summary, the probability of intersection of two events is the probability that both events occur simultaneously, and can be calculated using the formula P(A ∩ B) = P(A) x P(B|A) or P(A ∩ B) = P(A) x P(B) if the events are independent.