Question

A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and two balls are drawn at random (without replacement) from the bag which are both found to be red. Find the probability that the balls are drawn from the first bag. 

Answer 1

Let E₁ : event of selecting bag with 4 red and 4 black balls and, E₂ : event of selecting bag with 2 red and 6 black balls.

Also let E : event of selecting 2 red balls without replacement.