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Let {A},{B},{C} be three events such that {P}{({A})}={0}.{3},{

Question

Let $A, B, C$ be three events such that \displaystyle{P}{\left({A}\right)}={0}.{3},{P}{\left({B}\right)}={0}.{4},{P}{\left({C}\right)}={0}.{8},{P}{\left({A}\cap{B}\right)}={0}.{88},{P}{\left({A}\cap{C}\right)}={0}.{28},{P}{\left({A}\cap{B}\cap{C}\right)}={0}.{09}. If $P (A \cup B \cup C) \geq 0.75,$ then show that $0.23 \leq P (B \cap C) \leq 0.48 .$

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Let

A, B, C

be three events such that \displaystyle{P}{\left({A}\right)}={0}.{3},{P}{\left({B}\right)}={0}.{4},{P}{\left({C}\right)}={0}.{8},{P}{\left({A}\cap{B}\right)}={0}.{88},{P}{\left({A}\cap{C}\right)}={0}.{28},{P}{\left({A}\cap{B}\cap{C}\right)}={0}.{09}. If

P (A \cup B \cup C) \geq 0.75,

then show that

0.23 \leq P (B \cap C) \leq 0.48 .

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Question Text

Let

A, B, C

be three events such that \displaystyle{P}{\left({A}\right)}={0}.{3},{P}{\left({B}\right)}={0}.{4},{P}{\left({C}\right)}={0}.{8},{P}{\left({A}\cap{B}\right)}={0}.{88},{P}{\left({A}\cap{C}\right)}={0}.{28},{P}{\left({A}\cap{B}\cap{C}\right)}={0}.{09}. If

P (A \cup B \cup C) \geq 0.75,

then show that

0.23 \leq P (B \cap C) \leq 0.48 .