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  4. If A and B are two independent events such that P( barA)=0.75, P(A ∪ B)=0.65, and P ( B )=x, then find the value of x :

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Q. If $A$ and $B$ are two independent events such that $P(\bar{A})=0.75, P(A \cup B)=0.65$, and $P ( B )=x$, then find the value of $x$ :

KCETKCET 2022Probability - Part 2

Solution:

$P ( A )=\frac{1}{4}, P ( B )=\frac{3}{4}, P ( A \cup B )=\frac{13}{20}$
$\frac{1}{4}+ x -\frac{1}{4} \cdot x =\frac{13}{20}$
$\frac{3}{4} x-\frac{13}{20}-\frac{5}{20}=\frac{8}{20}$
$x=\frac{8}{20} \times \frac{4}{3}=\frac{8}{15}$