We have 2 opaque boxes, each containing 3 balls. One box has 2 red balls and 1 b

Question

We have 2 opaque boxes, each containing 3 balls. One box has 2 red balls and 1 blue ball, the other has 1 red ball and 2 blue balls. You pick a box at random and then pick one of the balls in that box at random. When you look at the ball it is red. (a) What is the probability that the remaining two balls in this box have the same colour? (b) You then randomly pick a ball from the remaining two balls in tills box, and it turns out to lie blue. What is the probability that the last ball in this box is also blue? Show working.

Explanation / Answer

Dear Student Thank you for using Chegg !! Given 2 boxes B1 and B2 (Suppose) B1 contains 2R and 1B balls B2 contains 1R and 2B balls Now 1 box is selected at random Prabability of selection of 1 box out of 2 is 1/2 Now out of 3 balls in the box, 1 red ball is selected (Number of ways is 2/3 for B1 and 1/3 for B2) Now for the remaining 2 balls of the box to have the same color (=> Box B2 was selected because only then after removal of red ball 2 blue balls of same color shall be left) Probability = (1/2)*(1/3) /[ (1/2)(1/3) + (1/2) (2/3)] = (1/6) / (1/2) = 1/3 Solution Now for the last ball to be also blue is imperative since (1/3) is the probability that the other 2 balls in the box is of the same color and first ball was red = (1/3) Solution

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