First box contains 6 Red balls, 4 Green Balls. Second box contains 7 Red Balls and 3 Green Balls. A ball is randomly picked from the first box and then put in the second box. Then a ball is randomly selected from the second box and then put in the first box. (a) What is the probability that a red ball is selected from the first box and a red ball is selected from the second box. (b) At the conclusion of the process, what is the probability that the number of red & green balls in the first box is identical to the numbers at the beginning.
(b)The only way the number of R&G balls in the first box will be same if either a red ball was picked from box 1 and then a red ball was picked from box 2 and put back on box 1, or the same process with green ball has to have happened.
Am I on the right track? Any help is much appreciated. I apologize for the fact that the title is a bit vague but could not come up with a better title.