Suppose 3 boxes contain Red, Green, and Blue marbles, denoted R, G, B, respectiv

Question

Suppose 3 boxes contain Red, Green, and Blue marbles, denoted R, G, B, respectively. Box 1 has 3 Red, 4 Green, and 3 Blue. Box 2 has 8 Red, 1 Green, and 1 Blue. Box 3 has 0 Red, 4 Green, and 1 Blue. Suppose a box is chosen at random, and then a marble is selected from the box. (a) If box 1 is selected, what is the probability a Green marble is drawn? (b) What is the probability a Blue marble is drawn from Box 3? (c) What is the probability a Red marble is drawn? (d) Suppose a Red marble is drawn. What is the probability it came from Box 2?

Explanation / Answer

Ans:

P(box 1)=P(box 2)=P(box 3)=1/3

a)P(green/box 1)=4/10=0.4

b)P(blue marble from box 3)=1/5

c)P(red)=P(red/box 1)*P(box 1)+P(red/box 2)*P(box 2)+P(red/box 3)*P(box 3)

=(3/10)*(1/3)+(8/10)*(1/3)+0*(1/3)

=0.367

d)

P(box 2/red)=P(red/box2)*P(box2)/P(red)=(8/10)*(1/3)/0.367=0.727

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