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 and are found to be both red. Find the probability that the balls are drawn from the first bag.

Explanation

`P(B_1) = 1/2 `

`P(B_2) = 1/2`

`P(R/B_1)= 4/8 = 1/2`

`P(R/B_2) = 2/8 = 1/4`

`P(B_1/R) = (P(B_1)P(R/B_1))/(P(B_1)P(R/B_1) + P(B_2)P(R/B_2))`

`= (1/2)/(1/2 + 1/4) = (2/4)/(2/4+1/4) `

`= 2/3`

Answer