Question

$Given$ that the drawn ball from $U_2$ is white, the probability that head appeared on the coin is

• A. $\frac{17}{23}$
• B. $\frac{11}{23}$
• C. $\frac{15}{23}$
• D. $\frac{12}{23}$

Answer 1

The correct option is D $\frac{12}{23}$

Required Probability $=P\left(H|W\right)=\frac{P(H\cap W)}{P\left(W\right)}$
$P(H,W)=\frac{1}{2}(\frac{3}{5}\times 1+\frac{2}{5}\times \frac{1}{2})=\frac{2}{5}$
$P\left(W\right)=\frac{1}{2}(\frac{3}{5}\times 1+\frac{2}{5}\times \frac{1}{2})=\frac{2}{5}+\frac{1}{2}(\frac{3}{10}\times 1+\frac{1}{10}\times \frac{1}{3}+\frac{6}{10}\times \frac{2}{3})=\frac{2}{5}+\frac{11}{30}=\frac{23}{30}$
$P\left(H|W\right)=\frac{12}{23}$