Two urns contain respectively 2 red 3 white and 3 red,5 white balls. One ball is drawn at random from the first urn and transferred into the second. A ball is now drawn from the second urn and it turns out to be red. What is the probability that the transferred ball was white?
1/17
9/17
8/17
none
Explanation:
According to the Bayes theorem,
p (no of way to drawn a ball from 2nd urns is red and ball transferred from 1 urns) =(3c1/5c1) $\times$ (3c1/9c1) =9/45.
Total=(2c1/5c1) $\times$ (4c1/9c1) +(3c1/5c1) $\times$ (3c1/9c1) =17/45.
So, probability = (9/45)/ (17/45) = 9/17.