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 minimum value of P(B∩C)?

P(A∩B) = P(A) + P(B) - P(A∪B) = 0.6 + 0.4 - 0.8 = 0.2. P(A∪B∪C) = P(A) + P(B) + P(C) - P(A∩B) - P(A∩C) - P(B∩C) + P(A∩B∩C). So 0.85 ≤ 0.6+0.4+0.5-0.2-0.3-P(B∩C)+0.2 = 1.2 - P(B∩C). Thus P(B∩C) ≤ 0.35. Also P(B∩C) ≥ P(A∩B∩C) = 0.2. So minimum value is 0.2.