Given, $P(A)=0.5, P(B)=0.4, P(A \cap B)=0.3$, then $P\left(A^{\prime} / B^{\prime}\right)$ is equal to

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Aicharya · Accepted Answer

Given $P(A)=0.5, P(B)=0.4$ and $P(A \cap B)=0.3$ To Find $P\left(A^{\prime} / B^{\prime}ight)=$ ? First, we find $P(A \cup B)$. $ \begin{gathered} \because P(A \cup B)=P(A)+P(B)-P(A \cap B) \ =0.5+0.4-0.3=0.6 \ P\left(B^{\prime}ight)=1-P(B)=1-0.4=0.6 \end{gathered} $ $\begin{aligned} P(A \cup B)^{\prime}= & 1-P(A \cup B) \ = & 1-0.6=0.4 \ \because P\left(A^{\prime} / B^{\prime}ight) & =\frac{P\left(A^{\prime} \cap B^{\prime}ight)}{P\left(B^{\prime}ight)} \ & =\frac{1-P(A \cup B)}{1-P(B)}=\frac{0.4}{0.6}=\frac{2}{3}\end{aligned}$

Given, $P(A)=0.5, P(B)=0.4, P(A \cap B)=0.3$, then $P\left(A^{\prime} / B^{\prime}\right)$ is equal to

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