Let `U_1` , and `U_2`, be two urns such that `U_1`, contains `3` white and `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 `U_1`, and put into `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, the probability of the drawn ball from `U_2,` being white is

Options

A. `17/23`
B. `11/23`
C. `15/23`
D. `12/23`

Answer

D

Explanation

`P((H)/(W))=(P(W//H)xxP(H))/(P(W//T).P(T)+(W//H).P(H))`
`=(1/2((3)/(2)xx1+2/5xx1/2))/(23//30)=12/23`