Question

Box 1 contains 8 blue balls and 7 red balls. Box 2 contains 9 blue balls and 8 red balls. If 3 balls are selected simultaneously from Box 1 and put into Box 2, what is the expected number of blue balls in Box 2?

Answer 1

There are 15 balls in total in Box 1 out of which 8 are blue and 7 are red.

So, the probability of picking a blue ball from Box 1 , P(B₁) = 8/15

And the probability of picking a red ball from Box 1, P(R₁) = 7/15

And there are 17 balls in Box 2 out of which 9 are blue and 8 are red.

3 balls are selected simultaneously from Box 1 and put into Box 2, then expected number of blue ball out of these 3 balls = 3* 8/15 = 1.6 ≃ 2

Hence the expected numbers of blue balls in Box 2 after putting 3 balls from box one = 9+2 =11