Answer: 0.667.
- A 0.667
- B 0.500
- C 0.750
- D 0.600
Correct answer: A. 0.667
Explanation: Total probability: P(E) = P(E|H)P(H) + P(E|H')P(H') = 0.9×0.4 + 0.3×0.6 = 0.36 + 0.18 = 0.54. Bayes: P(H|E) = P(E|H)P(H)/P(E) = 0.36/0.54 = 2/3 ≈ 0.667.
Venn diagram of the universal set U with events A and B, showing the intersection (A and B), the parts unique to each event, and the complement region outside both.
Concept context
Chance, events, conditional probability, and Bayes theorem