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  4. If A and B are two events such that P( barA)=0.3, P(B)=0.4 and P(A barB)=0.5, then P((B/A ∪ barB)) is equal to

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Q. If $A$ and $B$ are two events such that $P(\bar{A})=0.3, P(B)=0.4$ and $P(A \bar{B})=0.5$, then $P\left(\frac{B}{A \cup \bar{B}}\right)$ is equal to

Probability - Part 2

Solution:

$\Theta \quad P(\bar{A})=1-P(A)=0.3 \Rightarrow P(A)=0.7 $
$P(A \bar{B})=P(A)-P(A \cap B)=0.5 \Rightarrow P(A)-P(A \cap B)=0.2$
$\therefore \quad P\left(\frac{B}{A \cup \bar{B}}\right)=\frac{P(B \cap(A \cup \bar{B}))}{P(A \cup \bar{B})}=\frac{P(A \cap B)}{1-(P(B)-P(A \cap B))}=\frac{0.2}{0.8}=\frac{1}{4}$