Box 1 contains 3 red balls and 5 green balls. Box 2 contains 5 red balls and 3 g

Question

Box 1 contains 3 red balls and 5 green balls. Box 2 contains 5 red balls and 3 green balls. A ball is randomly selected from Box 1 and placed in box 2. Then a ball is again randomly selected from Box 2. What is the probability that red balls are selected from both boxes? (b) Box 1 contains 3 red balls and 5 green balls. Box 2 contains 5 red balls and 3 green balls. A ball is randomly selected from Box 1 and placed in box 2. Then a ball is again randomly selected from Box 2 and placed in box 1. What is the probability that after the end of the process, box 1 ends with 3 red balls and 5 green balls, the same number of red and green balls as in the beginning of the process?

Explanation / Answer

a)

Box 1 contains 3red balls and 5 green balls. Box 2 contains 5 red and 3 green balls

Probability of selecting red balls from both boxes = Probability of selecting red ball from box1* Probability of selecting red ball from box2 when red ball is selctected from box 1

Probability of selecting red ball from box1 = 3/(3+5) = 3/8

when red ball is selcted from box1 then no of red balls and balls in box 2 will increase by 1

Probability of selecting red ball from box2 when red ball is selctected from box 1 = 6/(6+3) = 6/9

Probability of selecting red balls from both boxes = (3/8)*(6/9) = 0.25

b)

Box 1 contains 3red balls and 5 green balls. Box 2 contains 5 red and 3 green balls

for Box 1 to remain with same number of red balls and green balls. same color should be pciked from box 1 and box2

Probability of selecting red balls from both boxes = 0.25 (clauclated in part a)

Probability of selecting green balls from both boxes = Probability of selecting green ball from box1* Probability of selecting green ball from box2 when green ball is selctected from box 1

Probability of selecting green ball from box1 = 5/(3+5) = 5/8

when green ball is selcted from box1 then no of green balls and balls in box 2 will increase by 1

Probability of selecting green ball from box2 when green ball is selctected from box 1 = 4/(6+3) = 4/9

Probability of selecting green balls from both boxes = (5/8)*(4/9) = 0.28

Probabililty of that the process ends up in same number of red and green balls =Probability of selecting green balls from both boxes+Probability of selecting red balls from both boxes = 0.25+0.28 = 0.53

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