There are 3 bags, each containing 5 white balls and 3 black balls. Also there are 2 bags, each containing 2 white balls and 4 black balls. A white ball is drawn at random. Find the probability that this white ball is from a bag of the first group.

Explanation

there are in total 5 bags and 3 are of first group and 2 are of 2nd group.

so probability of group 1=`3/5` and group 2=`2/5`

Probability of white ball from group 1=> `5/8`

Probability of white ball from group 2=>`2/6`

probability white ball was from group1=`(3/5xx5/8)/((3/5xx5/8)+(2/5xx2/6))=45/61`