Question

what does p(b|a) represent? choose the correct answer below a. the probability of event a and event b both occurring b. the probability of event a or event b or both occurring c. the probability of event b occurring after it is assumed that event a has already occurred d. the probability of event a occurring after it is assumed that event b has already occurred

Explanation:

• Option A: The probability of A and B both occurring is \( P(A \cap B) \), not \( P(B|A) \).
• Option B: The probability of A or B or both is \( P(A \cup B) \), not \( P(B|A) \).
• Option C: By the definition of conditional probability, \( P(B|A) \) is the probability of event B given that event A has already occurred.
• Option D: This would be \( P(A|B) \), not \( P(B|A) \).

Answer:

C. The probability of event B occurring after it is assumed that event A has already occurred