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. `13/30`
B. `23/30`
C. `19/30`
D. `11/30`

Answer

B

Explanation

`Hto1 "ball from"U_(1)"to" U_(2)`
`T to 2` ball from `U_(1) "to" U_(2)`
E: 1 ball drawn from `U_(2)`
`=1/2xx((3)/(5)xx1)+1/2xx((2)/(5)xx(1)/(2))+1/2xx((""^(3)C_(2))/(""^(5)C_(2))xx1/3)`
`+1/2xx((""^(3)C_(1).""^(2)C_(1))/(""^(5)C_(2))xx2/3)=23/30`