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There are four boxes, A, B C and D containing marbles. A contains 1 red, 6 white and 3 black marbles, B contains 6 red, 2 white and 2 black marbles, C contains 8 red, 1 white an 1 black marles, and D contains 6 white and 4 black marbles. One of the boxes is selected at random and a single marble is drawnfrom it. If the marble is red, what is the probability that it was drawn from the box A?

Answer»

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Solution :Let `E_1,E_2,E_3,E_4` be the events of selecting boxes A, B, C, D REPECTIVELY. Then,
`P(E_1)=P(E_2)=P(E_3)=P(E_4)=1/4`.
Let E = EVENT that the marble drawn is red. Then,
`P(E//E_1)=1/10,P(E//E_2)=6/10=3/5,P(E//E_3)=8/10=4/5,P(E//E_4)=0.`
`:. P(E_1//E)=(P(E//E_1).P(E_1))/(P(E//E_1).P(E_1)+P(E//E_2).P(E_2)+P(E//E_3).P(E_3)+P(E//E_4).P(E_4))`


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