# Probability problem

• Sep 20th 2010, 01:47 PM
ashamrock415
Probability problem
One box contains 6 red balls and 4 green balls, and a second box contains 7 red balls and 3green balls. A ball is randomly selected 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.

At the conclusion of the selection process, what is the probability that the numbers of red and green balls in the first box are identical to the numbers at the beginning?
• Sep 20th 2010, 02:01 PM
Plato
Quote:

Originally Posted by ashamrock415
One box contains 6 red balls and 4 green balls, and a second box contains 7 red balls and 3green balls. A ball is randomly selected 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. At the conclusion of the selection process, what is the probability that the numbers of red and green balls in the first box are identical to the numbers at the beginning?

What must sequence must happen to reach that conclusion?

Here is a hint: $R_1R_2\text{ or }G_1G_2$.