10 Imagine you are selected as a contestant on The Price is

10. Imagine you are selected as a contestant on The Price is Right. The host. Bob Barker. shows you three boxes with marbles in them. Box #1 contains 2 red. 3 white and 5 blue marbles. Box #2 contains 5 red. 3 white and 2 blue marbles. Lastly. Box #3 contains 3 red. 4 white and 3 blue marbles. One of Bob?s assistants will pick marbles from one of the boxes after they are hidden behind a curtain. if you correctly guess which box the marbles were picked from, you win a brand new car! Which box (or boxes) would you pick if ... a) one white and one blue marble are selected, with replacement? b) one red and one blue marble are selected, without replacement? c) one red, one white, and one blue marble are selected, without replacement?

Solution

a) One white and one blue are selected

P(one white and one blue from I box) = 0.3(0.5) = 0.15

P(one white and one blue from II box) = 0.3(0.2) = 0.06

P(one white and one blue from IIIbox)=0.4(0.3) = 0.12

-------------------------------------------------------------------------------

As prob is more for I box, better to select first box.

----------------------------------------------------------------------------------------------------------------------

b) P(one red and one blue from I box)=0.1

P(II box) = 0.1

P(III box) = 0.09

Hence I and II boxes are selected.

--------------------------------------------------------------------

c) 1R, 1W, 1B without replacement

I box prob = 2(3)(5)/10C3

II box = 5(3)(2)/10C3

III Box = 3(3)(4)/10C3

As prob is more for I and II Box, they would be selected