Question

A bag A contains 2 white and 3 red balls and bag B contains 4 white and 5 red balls.One ball is drawn at random from a randomly chosen bag and is found to be red. The probability that it was drawn from bag B was-

• A. $5/14$
• B. $5/16$
• C. $5/18$
• D. $25/52$

Answer 1

The correct option is D $25/52$

Given that ball is red probability that it is from Bag B
$\frac{\frac{1}{2}\times \frac{5}{9}}{\frac{1}{2}\times \frac{3}{5}\times \frac{1}{2}\times \frac{5}{9}}=\frac{\frac{5}{9}}{\frac{3}{5}+\frac{5}{9}}=\frac{25}{52}\left(D\right)$