Question

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

Explanation:

In probability, the notation \( P(B|A) \) is the conditional probability formula. By definition, \( P(B|A)=\frac{P(A\cap B)}{P(A)}\) (where \( P(A)> 0\)), which represents the probability of event \( B \) occurring given that event \( A \) has already occurred.

• Option A: Incorrect. The formula \( P(A|B)\) represents the probability of event \( A \) occurring after event \( B \) has occurred.
• Option B: Correct. As per the definition of conditional probability.
• Option C: Incorrect. The probability of event \( A \) or event \( B \) or both occurring is \( P(A\cup B)=P(A)+P(B)-P(A\cap B)\).
• Option D: Incorrect. The probability of event \( A \) and event \( B \) both occurring is \( P(A\cap B)\).

Answer:

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