Let U1 and U2 be two urns such that U1 contains 3 white and 2 red balls, and U2 contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U1 and put into U2. However, if tail appears then 2 balls are drawn at random from U1 and put into U2. Now 1 ball is drawn at random from U2.Given that the drawn ball from U2 is white, the probability that head appeared on the coin

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`