Question

Multiplication theorem of probability is.

• A. \( P(A \cap B) = P(A) \cdot P(B) \)
• B. \( P(A \cap B) = P(A) + P(B) - P(A \cup B) \)
• C. \( P(A \cap B) = P(A) \cdot P(B / A) \)
• D. None of these

Hint:

The multiplication theorem is crucial when events are not independent, and we need to account for the likelihood of one event occurring after another.

Answer 1

The Correct Option is C

The multiplication theorem of probability, which is used to find the probability of the intersection of two events \( A \) and \( B \), states that: \[ P(A \cap B) = P(A) \cdot P(B / A). \] This formula is derived from the definition of conditional probability. The conditional probability \( P(B / A) \) is the probability of event \( B \) occurring given that event \( A \) has already occurred. Therefore, the joint probability of \( A \) and \( B \) happening is the product of the probability of \( A \) and the conditional probability of \( B \) given \( A \).