Question

Given P(A) = 0.4 and P(B) = 0.8, do the following. (For each answer, enter a number.)

(a)If A and B are independent events, compute P(A and B).
(b)If P(A | B) = 0.7, compute P(A and B).

Answer 1

If events A and B are independent, the probability of both events occurring can be calculated by multiplying their individual probabilities. When P(A | B) is given, we can use the conditional probability formula to calculate P(A and B).

Step-by-step explanation:

If events A and B are independent, the probability of both events occurring, P(A and B), can be calculated by multiplying their individual probabilities: P(A) × P(B). So, in this case, P(A and B) = 0.4 × 0.8 = 0.32.

To compute P(A and B) when P(A | B) is given, we can use the conditional probability formula: P(A and B) = P(A | B) × P(B). Given that P(A | B) = 0.7, we can calculate P(A and B) as P(A and B) = 0.7 × 0.8 = 0.56.