A box contains 4 white and 5 black balls. A ball is drawn at random and its colour is noted. A ball is then put back in the box along with two additional balls of its opposite colour. If a ball is drawn again from the box, then the probability that the ball drawn now is black, is

Options

A. `(7)/(11)`
B. `(5)/(11)`
C. `(53)/(99)`
D. `(48)/(99)`

Answer

C

Explanation

Consider the following events :
`E_(1)`=Ball drawn from the box is white
`E_(2)`=Ball drawn from the box is black
A= Getting a black ball from the box after replacing the drawn ball with two balls of opposite colour
`P(E_(1))=(4)/(9),P(E_(2))=(5)/(9),P(A//E_(1))=(7)/(11),P(A//E_(2))=(5)/(11)`
`therefore P(A)=P(E_(1))P(A//E_(1))+P(E_(2))P(A//E_(2))`
`=(4)/(9)xx(7)/(11)+(5)/(9)xx(5)/(11)=(53)/(99)`