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  4. If A and B are two events of a sample space S such that P(A) = 0.2, P(B) = 0.6 and P(A | B) = 0.5 then P(A’| B)=

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Q. If A and B are two events of a sample space S such that P(A) = 0.2, P(B) = 0.6 and P(A | B) = 0.5 then P(A’| B)=

KCETKCET 2019Probability

Solution:

$P\left(A\right)=0.2, P\left(B\right)=0.6$
$\Rightarrow \, P\left(A |B\right)=0.5$
$\frac{P\left(A\cap B\right)}{P\left(B\right)}=0.5$
$\Rightarrow \, P\left(A\cap B\right)=0.5\left(P\left(B\right)\right)=\left(0.5\right)\left(0.6\right)=0.3$
$P\left(A ' | B\right)=\frac{P\left(A'\cap B\right)}{P\left(B\right)}=\frac{P\left(B\right)-P\left(A\cap B\right)}{P\left(B\right)}$
$=\frac{0.6-0.3}{0.6}=\frac{0.3}{0.6}=\frac{3}{6}=\frac{1}{2}$

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