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The probabilities of three events A, B, ...

The probabilities of three events A, B, C are `P(A)=0.6, P(B)=0.4 and P(C )=0.5`. If `P(A cup B)=0.8, P(A cap C)=0.3, P(A cap B cap C)=0.2 and P(A cup B cup C) ge 0.85`, show that, `0.2 le P(B cap C) le 0.35`.

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