Question

An urn contains 5 white and 7 black balls. A second urn contains 7 white and 8 black balls. One ball is transfered from the 1st urn to the 2nd urn without noticing its colour. A ball is now drawn at random from the 2nd urn. The probability that it is white is

• A. $\frac{8}{92}$
• B. $\frac{89}{192}$
• C. $\frac{9}{92}$
• D. $\frac{98}{192}$

Answer 1

The correct option is B $\frac{89}{192}$

The possible cases of the second ball being white:
(i) First ball is white and so is the second: $\frac{5}{12}\ast \frac{8}{16}=\frac{40}{192}$
(ii) First is black and the second is white: $\frac{7}{12}\ast \frac{7}{16}=\frac{49}{192}$
Hence, the required probability = $\frac{40}{192}+\frac{49}{192}=\frac{89}{192}$