Consider two boxes containing marbles of differing colors BOXA 2 red 3 green BOX

Question

Consider two boxes containing marbles of differing colors BOXA 2 red 3 green BOXB 3 red lgreen_ Total: 5 marbles Total: 4 marbles The exterior of the boxes are identical and we are never allowed to inspect the interior of the boxes. The boxes are randomized so that we don't know which box is which. We will make one draw at random from EACH box. Answer the following Define events: Ai: the first draw will be made from box A Bi: the first draw will be made from box B Ri: the first draw will be red R2: the second draw will be red Gi: the first draw will be green G2: the second draw will be green

Explanation / Answer

box A box B red 2 3 green 3 1 marbles 5 4 in box A: P(marbles will be of same color) =(1/2)*(COMBIN(2,2)+COMBIN(3,2))/COMBIN(5,2) 0.2 in box B: P(marbles will be of same color) =(1/2)*(COMBIN(3,2)+0)/COMBIN(4,2) 0.25 hence, required prob.: =0.2+0.25 0.45

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