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Refer to question 41 above. If a white ball is selected, what is the probability that it come from ltbr?. (i) Bag II?(ii) Bag III?

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SOLUTION :REFERRING to the PREVIOUS solution, using Bay's theorem, we have
(i) `P(E_(2)//F)=(P(E_(2))cdotP(F//E_(2)))/(P(E_(1)cdotP(F/E_(1))+P(E_(2))cdotP(F//E_(2))+P(E_(3))cdotP(F//E_(3)))`
`=(2/6cdot1/3)/(1/6cdot0+2/6cdot1/3+3/6cdot1)=(2/18)/(2/18+3/6)`
`(2//8)/((2+9)/(18))=2/11`
(i) `P(E_(3)//F)=(P(E_(3))cdotP(F//E_(3)))/(P(E_(1)cdotP(F/E_(1))+P(E_(2))cdotP(F//E_(2))+P(E_(3))cdotP(F//E_(3)))`
`=(3/6cdot1)/(1/6cdot0+2/6cdot1/3+3/6cdot1)`
`=(3/6)/(2/18+3/6)=(3//6)/(2/18+9/18)=9/11`


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