In case of conditional probability (A and B) = ?

The correct answer is: A. P(B) × P(A/B).

Conditional probability is the probability of event A occurring given that event B has already occurred. It is calculated by dividing the probability of both events occurring by the probability of event B occurring.

In other words, P(A|B) = P(A and B) / P(B).

Option A is the correct answer because it is the formula for conditional probability. Option B is incorrect because it is the formula for joint probability. Option C is incorrect because it is the formula for marginal probability. Option D is incorrect because it is not a valid formula for probability.

Here is a more detailed explanation of each option:

• Option A: P(B) × P(A/B)

This is the formula for conditional probability. Conditional probability is the probability of event A occurring given that event B has already occurred. It is calculated by dividing the probability of both events occurring by the probability of event B occurring.

In other words, P(A|B) = P(A and B) / P(B).

• Option B: P(B) × P(A)

This is the formula for joint probability. Joint probability is the probability of both events A and B occurring. It is calculated by multiplying the probability of event A occurring by the probability of event B occurring.

In other words, P(A and B) = P(A) × P(B).

• Option C: P(A) + P(B)

This is the formula for marginal probability. Marginal probability is the probability of event A occurring, regardless of whether or not event B occurs. It is calculated by adding the probability of event A occurring and the probability of event B occurring, minus the probability of both events occurring.

In other words, P(A) = P(A and B) + P(A and not B).

• Option D: None of these

This is the correct answer because it is not a valid formula for probability.