One box contains five red balls and five green balls, and a second box contains

Question

One box contains five red balls and five green balls, and a second box contains six red balls and four green balls. A ball is randomly chosen from the first box and placed in the second box. Then a ball is randomly selected from the second box and placed in the first box.
a.) What is the probability that a green ball is selected from the first box and a green ball is selected from the second box?
b.) At the conclusion of the selection process, what is the probability that the numbers of red and green balls in the first box are different then the numbers at the beginning?

Explanation / Answer

Box 1: 5 red and 5 green

Box 2: 6 red and 4 green

a) P(green first and green second) = 5/10 x 5/11

= 5/22

b) P(the numbers of red and green balls in the first box are different than the numbers at the beginning) = 1 - P(green first and green second) - P(red first and red second)

= 1 - 5/22 - 5/10 x 7/11

= 1 - 5/22 - 7/22

= 5/11

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