Question

$If \ P(A)=\frac {6}{11},\ P(B)=\frac {5}{11}\ and\ P(A∪B) =Find:$

1. $P(A∩B)$
2. $P(A|B)$
3. $P(B|A)$

Answer 1

$(i) P(A∪B)=P(A)+P(B)–P(A∩B)$

$P(A∩B)=\frac {7}{11}$

⇒ $\frac {6}{11}+\frac {5}{11}-P(A∩B) = \frac {7}{11}$

⇒ $P(A∩B)=\frac {6}{11}+\frac {5}{11}-\frac {7}{11}$

$P(A∩B) =\frac {4}{11}$

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$(ii)P(A|B)=\frac {P(A∩B)}{P(B)}$

$P(A|B)=\frac {4/11}{5/11}$

$P(A|B) =\frac 45$

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$(iii)P(B|A)=\frac {P(A∩B)}{P(A) }$

$P(B|A)=\frac {4/11}{6/11 }$

$P(B|A)=\frac {4}{6 }$

$P(B|A) =\frac 23$