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Question
There are two boxes I and II. Box I contains 3 red and 6 Black balls. Box II contains 5 red and black balls. One of the two boxes, box I and box II is selected at random and a ball is drawn at random. The ball drawn is found to be red. If the probability that this red ball comes out from box II is ' a find the value of n
Solution
E1 = selecting box I
E2 = selecting box II
A = getting a red ball from the selected box
`"P" (E_1) = 1/2 , "P"("E"_1) = 1/2`
`"P"("A"/"E"_1) = 3/9 = 1/3`
`"P"("A"/"E"_2) = (5)/(n+5)`
Using Baye's theorem
`"P"("E"_2/"A") = ("P"("E"_2)"P"("A"/"E"_2))/("P"("E"_1)"P"("A"/"E"_1)+ "P"("E"_2)"P"("A"/"E"_2))`
`(3)/(5) = (1/2 xx (5)/(n+5))/(1/2xx1/3+1/2xx5/(n+5)`
`(3)/(5) = (15)/(n+20)`
(n+20)3= 75
3n = 15
n = 5
Therefore, the value of n is 5.
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