Question

Given P(A) = 0.4, P(B) = 0.5, P(A | B) = 0.3, do the following.

a. Compute P(A ∩ B).
b. Compute P(A ∪ B).
a. 0.12, 0.7
b. 0.15, 0.8
c. 0.18, 0.9
d. 0.21, 1.0

Answer 1

To find P(A ∩ B), you multiply P(A | B) by P(B), resulting in 0.15. P(A ∪ B) is calculated by adding P(A) and P(B) and then subtracting P(A ∩ B), equalling 0.75. The correct final answer is 0.15 for the intersection and 0.75 for the union. Option B is the correct answer.

Step-by-step explanation:

The question asks for the computation of both the intersection and union probabilities of events A and B, given P(A) = 0.4, P(B) = 0.5, and P(A | B) = 0.3. The probability of A and B both happening, noted as P(A ∩ B), can be found using conditional probability: P(A ∩ B) = P(A | B) × P(B), which is 0.3 × 0.5 = 0.15.

For the probability of either A or B happening, P(A ∪ B), we use the formula: P(A) + P(B) - P(A ∩ B), so it's 0.4 + 0.5 - 0.15 = 0.75. Therefore, the correct choice is b. 0.15, 0.8, which is a small error in the given options; the union should be 0.75.