Three bags contain balls as shown in the table below: Bag Number of White balls Number of Black balls Number of Red balls I 1 2 3 II 2 1 1 III 4 3 2 A bag is chosen at random and two balls are drawn from it. They happen to be white and red. What is the probability that they came from the III bag?

Explanation

`P((A_i)/B)=(P(B/A_i)P(A_i))/(sumP(B/A_i)P(A_i)`

`P(B/A_2)=(2C_1*1C_1)/(7C_2)=2/21`

`P(B/A_3)=(4C_1*3C_1)/(12C_2)=2/11`

`P(A_1/B)=(P(B/A_1)P(A_1))/(sumP(B/A)*P(a)`

`=(1/5)/(1/5+2/11+2/21)`

`=231/551`.