The probabilities of three events A, B, and C are P(A) = 0.6, P(B) = 0.4, and P(C ) = 0.5. If P(A∪B) = 0.8, P(A∩C)=0.3, P(A∩B∩C)=0.2, and P(A∪B∪C)≥0.85, then find the range of P(B∩C).

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The probabilities of three events A, B, and C are P(A) = 0.6,

Question

The probabilities of three events A, B, and 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 $P (A \cup B \cup C) \geq 0.85$ , then find the range of $P (B \cap C)$ .

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The probabilities of three events A, B, and 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) \geq 0.85

, then find the range of

P (B \cap C)

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Question Text

The probabilities of three events A, B, and 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) \geq 0.85

, then find the range of

P (B \cap C)