Question

A and B are two events such that P(A) = 1/3, P(B)=1/4, P(A+B)=1/2 then P(B/A) is equal to
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Answer 1

$\huge\boxed{\underline{\underline{\green{Solution}}}} </p><p>$

It is given that

$P(A) = \frac{1}{3} \: , P(B)= \frac{1}{4} \: , P(A+B)= \frac{1}{2}$

Now

$P(A+B)=P(A) + P(B) - P(A \cap \: B)$

So

$P(A \cap \: B) = \frac{1}{3} + \frac{1}{4} - \frac{1}{2} = \frac{1}{12}$

So

$P( \frac{ B}{A } )$

$= \frac{P(A \cap \: B)}{P(A)} \:$

$= \frac{ \frac{1}{12} }{ \frac{1}{3} }$

$= \frac{3}{12} = \frac{1}{4}$

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