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

# 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

1. A

$\frac{7}{11}$

2. B

$\frac{5}{11}$

3. C

$\frac{53}{99}$

4. D

$\frac{48}{99}$

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### Solution:

Consider the following events:

Ball drawn from the box is white

Ball drawn from the box is black

Getting a black ball from the box after replacing the drawn ball with two balls of opposite colour

$P\left({E}_{1}\right)=\frac{4}{9},P\left({E}_{2}\right)=\frac{5}{9},P\left(A/{E}_{1}\right)=\frac{7}{11},P\left(A/{E}_{2}\right)=\frac{5}{11}$

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