A bag `X` contains `2` white and `3` black balls and another bag `Y` contains `4` white and `2` black balls. One bag is selected at random and a ball is drawn from it. The, the probability chosen to be white is

Options

A. a) `2/15`
B. b) `7/15`
C. c) `8/15`
D. d) `14/15`

Answer

c) `8/15`

Explanation

Let,


`E_1=` Event of ball is drawn from bag `X`


`E_2=` Event of ball is drawn from bag `Y`


`E=` Event of white ball drawn


`P(E_1) =P(E_2)= 1/2`


`P(E/(E_1)) = 2/5, P(E/(E_2)) = 4/6 = 2/3`


We know,


`P(E) = P(E_1).P(E/(E_1)) +P(E_2).P(E/(E_2))`


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