A, B and C are three events such that P(A) = 0.6, P(B) = 0.4, P(C) = 0.5, P(A∪B) = 0.8, P(A∩C) = 0.3 and P(A∩B∩C) = 0.2 and P(A∪B∪C) ≥ 0.85. What is the maximum value of P(B∩C)?
A.0.1
B.0.2
C.0.35✓ Correct
D.0.45
Explanation
From P(A∪B∪C) ≤ 1: 1.2 - P(B∩C) ≥ P(A∪B∪C), and using inclusion-exclusion with P(A∪B∪C) at maximum being limited. From the equation P(A∪B∪C) = 1.2 - P(B∩C), since P(A∪B∪C) ≥ 0.85, P(B∩C) ≤ 0.35. Therefore maximum value of P(B∩C) is 0.35.
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