What is the multiplication rule for independent events?

What is the multiplication rule for independent events?

• A. P(A ∩ B) = P(A) + P(B)
• B. P(A ∩ B) = P(A)P(B)
• C. P(A ∩ B) = max(P(A), P(B))
• D. P(A ∩ B) = P(A) - P(B)

Answer: (B)

When two events are independent, the chance that both occur is the product of their individual probabilities. The likelihood of A and B happening together is P(A ∩ B) = P(A) × P(B). This captures the idea that knowing B did occur doesn’t change how likely A is, and vice versa. For example, flip a fair coin (P(A) = 0.5) and roll a fair die (P(B) = 1/6). The probability both happen is 0.5 × 1/6 = 1/12 ≈ 0.0833. The other expressions don’t describe the intersection probability in general: addition is related to the probability of the union (with a correction for overlap), the maximum isn’t the intersection, and subtraction isn’t a rule for the joint probability of independent events.

When two events are independent, the chance that both occur is the product of their individual probabilities. The likelihood of A and B happening together is P(A ∩ B) = P(A) × P(B). This captures the idea that knowing B did occur doesn’t change how likely A is, and vice versa.

For example, flip a fair coin (P(A) = 0.5) and roll a fair die (P(B) = 1/6). The probability both happen is 0.5 × 1/6 = 1/12 ≈ 0.0833.

The other expressions don’t describe the intersection probability in general: addition is related to the probability of the union (with a correction for overlap), the maximum isn’t the intersection, and subtraction isn’t a rule for the joint probability of independent events.