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

It is given that `P(A)=frac{6}{11}, P(B)=frac{5}{11}`, and `P(A cup B)=frac{7}{11}`

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


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

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

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

(ii) It is known that, `P(A | B)=frac{P(A cap B)}{P(B)}`

`Rightarrow P(A | B)=frac{frac{4}{11}}{frac{1}{5}}=frac{4}{5}`

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