If A and B are any two events such that P(B) = P(A and B), then which of the following is correct

The correct option is P(A|B) = 1 (represented in the options as P(A—B) = 1).

To understand why this is correct, let us analyze the conditional probability formula. The conditional probability of an event A occurring given that event B has already occurred is defined as:

$$P(A|B)=\frac{P(A\cap B)}{P(B)}$$

Here, $P(A\cap B)$ represents the probability of both events A and B occurring, which is given in the question as P(A and B).

According to the problem statement, we are given the condition:
$$P(B)=P(A\cap B)$$

Substitute this equality into the numerator of our conditional probability formula:

$$P(A|B)=\frac{P(B)}{P(B)}$$

Assuming $P(B)>0$, dividing $P(B)$ by itself yields:
$$P(A|B)=1$$

Thus, the conditional probability of event A given event B is equal to 1. This matches the notation P(A—B) = 1 in the options.