Question

The probability of the drawn ball from $U_2$ being white $is$

• A. $\frac{13}{30}$
• B. $\frac{23}{30}$
• C. $\frac{19}{30}$
• D. $\frac{11}{30}$

Answer 1

The correct option is B $\frac{23}{30}$

$P\left(W\right)=P(H,W)+P(T,W)$

If head comes then W or R from $U_1$ and $U_2$ will contain 2W or 1W1R

$P(H,W)=\frac{1}{2}(\frac{3}{5}\times 1+\frac{2}{5}\times \frac{1}{2})=\frac{2}{5}$

If tail comes, then WW or RR or WR from $U_1$ and $U_2$ will contain 3W or 1W2R or 2WR

$P(T,W)=\frac{1}{2}(\frac{3}{10}\times 1+\frac{1}{10}\times \frac{1}{3}+\frac{6}{10}\times \frac{2}{3})=\frac{11}{30}$

$P\left(W\right)=\frac{2}{5}+\frac{11}{30}=\frac{23}{30}$