Question

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)=

• A. $\frac{1}{2}$
• B. $\frac{5}{12}$
• C. $\frac{5}{16}$
• D. $\frac{16}{21}$

Answer 1

Answer: (A)

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