Box 1 contains six red balls and four green balls Box 2 cont

Box 1 contains six red balls and four green balls. Box 2 contains seven red balls and three 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 six red balls and four green balls, the same number of red and green balls as in the beginning of the process?

Solution

Box 1 contains six red balls and four green balls. Box 2 contains seven red balls and three green balls.

Now, 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.

Thus, the probability that after the end of the process, box 1 ends with six red balls and four green balls is:

6/10*8/11

=0.44