Below are three boxes containing black and white balls. The number of each color

Question

Below are three boxes containing black and white balls. The number of each color is noted inside the box. Draw a ball from box 1 and place it in box 2. Then draw a ball from box 2 and place it in box 3. Finally draw a ball from box 3. Box 1 3 white 2 black Box 2 2 white 2 black Box 3 1 white 2 black a) What is the probability that the last ball, drawn from box 3, is white? 19/50 (Type a simplified fraction.) b) What is the probability that the last ball drawn is black? (Type a simplified fraction.)

Explanation / Answer

a) probability =P(first ball white*second ball white*third ball white+first ball white *second ball black*third ball is white+

first ball black *second ball black*third ball is white+first ball black *second ball white*third ball is white)

=(3/5)*(3/5)*(2/4)+(3/5)*(2/5)*(1/4)+(2/5)*(3/5)*(1/4)+(2/5)*(2/5)*(2/4)=36/100=19/50

b)probability =1-19/50 =31/50

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