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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. - Mathematics

Question

Sum

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.

Concept: Probability Examples and Solutions
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