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

It means both the time same colour ball are excahnged.

Prob of selecting red ball both time = (6/10) * (8/11) = 0.4364

Prob of selecting green ball both time = (4/10) * (4/11) = 0.1455

Required Prob = 0.4364 + 0.1455 = 0.5819