If `P (A) =6/(11)`, `P(B) =5/(11)`and `P(AuuB)=7/(11)`, find(i) `P(AnnB)` (ii) `P(A|B)` (iii) `P(B|A)`

Explanation

We have `P(A)=frac{6}{11}, P(B)=frac{5}{11},` and `P(A cup B)=frac{7}{11}`

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(i) P(A cup B)=frac{7}{11}`

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therefore P(A)+P(B)-P(A cap B)=frac{7}{11} `

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Rightarrow frac{6}{11}+frac{5}{11}-P(A cap B)=frac{7}{11} `

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Rightarrow P(A cap B)=frac{11}{11}-frac{7}{11}=frac{4}{11}`

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(ii) P(A |B)=frac{P(A cap B)}{P(B)}`

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