If the probability of event A is 0.6 and event B is independent with P(B) = 0.5, what is P(A and B)?

If the probability of event A is 0.6 and event B is independent with P(B) = 0.5, what is P(A and B)?

• A. 0.60
• B. 0.15
• C. 0.50
• D. 0.30

Answer: (D)

When two events are independent, the chance that both happen is the product of their individual probabilities. So P(A and B) = P(A) × P(B) = 0.6 × 0.5 = 0.30. This matches the value for the probability of both A and B occurring. The other numbers would represent either just one event happening (0.6 or 0.5) or don’t align with the product rule under independence, so they’re not the probability of both occurring.

When two events are independent, the chance that both happen is the product of their individual probabilities. So P(A and B) = P(A) × P(B) = 0.6 × 0.5 = 0.30. This matches the value for the probability of both A and B occurring. The other numbers would represent either just one event happening (0.6 or 0.5) or don’t align with the product rule under independence, so they’re not the probability of both occurring.