Question

Let A, B, C be three events such that :
$P\left(A\right)=0.3,P\left(B\right)=0.4,P\left(C\right)=0.5,P(A\cap B^{{}^{\prime }})=0.2,P(B\cap C)=0.3,P(A^{{}^{\prime }}\cap B^{{}^{\prime }}\cap C^{{}^{\prime }})=0.3$ and $P\left(A\cap B|C^{{}^{\prime }}\right)=0.1$. Find the value of $P\left(B^{{}^{\prime }}|C^{{}^{\prime }}\right)$

• A. $\frac{1}{5}$
• B. $\frac{2}{5}$
• C. $\frac{3}{5}$
• D. $\frac{4}{5}$

Answer 1

The correct option is B $\frac{2}{5}$

$\left(\frac{B^1}{C^1}\right)=\frac{P(B^1\cap C^1)}{P\left(C^1\right)}=\frac{1-0.3}{1-0.5}1-P\frac{B\cap C}{P\left(C\right)}$

$P\left(B^1/C^1\right)=1-0.3/0.5=\frac{0.2}{0.5}=\frac{2}{5}$