CA Foundation · Quantitative Aptitude · Probability
For events A and B, P(A) = 0.6, P(B) = 0.5 and P(A ∪ B) = 0.8. What is P(B | A)?
P(B | A) is 1/2. First find the intersection using the addition rule: 0.6 + 0.5 - 0.8 = 0.3. Then divide by P(A): 0.3/0.6 = 0.5. Dividing by P(B) would wrongly give P(A | B), which is 0.6.
- A1/2
- B2/3Correct
- C3/4
- D1/3
Explanation
P(A∩B) = P(A) + P(B) - P(A∪B) = 0.6 + 0.5 - 0.8 = 0.3. So P(B|A) = 0.3/0.6 = 0.5. Check: 0.3/0.6 = 1/2, so the key is 1/2. The distractor 3/5 type errors arise from dividing by P(B) instead, giving P(A|B) = 0.3/0.5 = 3/5.
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