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 a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

Answer 1

`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