Question

One bag contains 5 white and 4 black balls. Another bag contains 7 white and 9 black balls. A ball is transferred from the first bag to the second and then a ball is drawn from second. The probability that the ball is white is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Let a white ball be transferred from the first bag to the second. The Probability of selecting a white ball from the first bag = $\frac{5}{9}$
Now the second bag has 8 white and 9 black. The probability of selecting white ball from the second bag = $\frac{8}{17}$
Hence required probability = $\frac{5}{9}\times \frac{8}{17}=\frac{40}{153}$
If a black ball be transferred from the first bag to the second, then the probability = $\frac{4}{9}\times \frac{7}{17}=\frac{28}{153}$
Therefore required probability = $\frac{40}{153}+\frac{28}{153}=\frac{4}{9}$