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Q. 4.     Evaluate  P(A\cup B),  if 2P(A)=P(B)=\frac{5}{13}  and  P(A\mid B)=\frac{2}{5} 

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Given in the question 2P(A)=P(B)=\frac{5}{13}  and  P(A\mid B)=\frac{2}{5} 

We know that:

P ( A | B ) = \frac{p(A\cap B)}{P(B)}

\frac{2}{5} = \frac{p(A\cap B)}{\frac{5}{13}}

\frac{2\times 5}{5\times 13} = p(A\cap B)

p(A\cap B)=\frac{2}{ 13}

Use, p(A\cup B)=p(A)+p(B)-p(A\cap B)

p(A\cup B)=\frac{5}{26}+\frac{5}{13}-\frac{2}{13}

p(A\cup B)=\frac{11}{26}

 

 

 

Posted by

seema garhwal

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