If P(notA)=0.7,P(B)=0.7\: \: and\: \: P(B/A)=0.5, then find P(A/B).

 

 

 

 
 
 
 
 

Answers (1)

Given P(\bar{A})=0.7\: \: ,\: P(B)=0.7

P\left ( \frac{B}{A} \right )=\frac{P(A\cap B)}{P(A)}

0.5=\frac{P(A\cap B)}{0.3}

\Rightarrow P(A\cap B)=0.15\: \: \: \: \: \left [ \because P(\bar A)=0.7\: then\: P(A=0.3) \right ]

Also we know,

P\left (\frac{A}{B} \right )=\frac{P(A\cap B)}{P(B)}

=\frac{0.15}{0.7}=\frac{3}{14}

and P(A\cup B)=P(A)+P(B)-P(A\cap B)

=0.3+0.7-0.15\Rightarrow 0.85

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