1.

Three urns A, Band C contain 6 red and 4 white, 2 red and 6 white, and 1 red and 5 white balls respectively. An um is chosen at random and a ball is drawn. If the ball drawn is found to be red, find the. probability that the ball was drawn from the urn A.

Answer»

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SOLUTION :Let `E_1,E_2and E_3` be the events of choosing the urns A,B and C RESPECTIVELY, and let E be the event of drawing a red ball. Then,
`P(E_1)=P(E_2)=P(E_3)=1/3`
`P(E/E_1)=6/10,P(E/E_2)=2/8,and P(E/E_3)=1/6`.
Required probability `=P(E_1/E)`
`=(P(E_1)XXP(E/E_1))/(P(E_1)xxP(E/E_1)+P(E_2)xxP(E/E_2)+P(E_3)xxP(E/E_3))`
`=((1/3xx6/10))/((1/3xx6/10)+(1/3xx2/8)+(1/3xx1/6))=36/61`.


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