Using the total probability rule, we can compute the P(B):
P(B) = [P(B | A) × P(A)] + [P(B | AC) × P(AC)]
P(B) = [0.5 × 0.4] + [0.2 × 0.6] = 0.32
Using Bayes’ formula, we can solve for P(A | B):
P(A | B) = [ P(B | A) ÷ P(B) ] × P(A) = [0.5 ÷ 0.32] × 0.4 = 0.625
