Let $U_1$ and $U_2$ be two urns such that $U_1$ contains 3 white 2 red balls, and $U_2$ contains only 1 white ball. A fair coin is tossed. IF head appears then 1 ball is drawn at random from urn $U_1$ and put onto $U_2$. However, if tail appears then 2 balls are drawn at random from $U_1$ and put into $U_2$. Now, 1 ball is drawn at random from $U_2$. Then probability of the drawn ball from $U_2$ being white is

$\frac{23}{30}$

By total probability theorem

Required probability $=\frac{1}{2}× \left(\frac{3}{5}×1 +\frac{2}{5}×\frac{1}{2}\right)+\frac{1}{2}\left(\frac{^3C_2}{^5C_2}×1+\frac{^2C_2}{^5C_2}×\frac{1}{3}+\frac{^3C_1×{^2C}_1}{^5C_2}×\frac{2}{3}\right)$

$=\frac{23}{30}$