The prob(A|B)) is the same as?

a. prob(B|A)

b. prob(A U B)

c. prob(A*B)

d. none of the above

1 answer

The notation \( P(A|B) \) represents the conditional probability of event \( A \) given that event \( B \) has occurred. This is not the same as any of the options provided, so the correct answer would be:

d. none of the above

To clarify, the relationships between these probabilities are as follows:

  • \( P(A|B) = \frac{P(A \cap B)}{P(B)} \) (not equal to \( P(B|A) \), which would be \( \frac{P(A \cap B)}{P(A)} \)).
  • \( P(A \cup B) \) refers to the probability that at least one of the events occurs, which is also not equal to \( P(A|B) \).
  • \( P(A \cap B) \) represents the joint probability of both events occurring, which is not the same as the conditional probability \( P(A|B) \).