1.

Three bags contain balls as shown in the tablebelow:BagNumber of White ballsNumber of Black ballsNumber of Red ballsI123II211III432A bagis chosen at random and two balls are drawn from it. They happen to be whiteand red. What is the probability that they came from the III bag?

Answer» `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`.


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