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, than 1 ball is drawn at random for `Us_(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)`
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

D

Explanation

By total probability theorem
Required probability `=(1)/(2)xx((3)/(5)xx1+(2)/(5)xx(1)/(2))+(1)/(2)((.^(3)C_(2))/(.^(5)C_(2))xx1+(.^(2)C_(2))/(.^(5)C_(2))xx1+(.^(2)C_(2))/(.^(5)C_(2))xx(1)/(3)+(.^(3)C_(1)xx.^(2)C_(1))/(.^(5)C_(2))xx(2)/(3))`
`=(23)/(30)`