There are 3 bags, each containing a white balls and b black balls. We are to randomly take one ball from the first bag and put it in the second bag.

There are 3 bags, each containing a white balls and b black balls. We are to randomly take one ball from the first bag and put it in the second bag. After that, we randomly take one ball from the second bag and put it in the third bag. Finally, we randomly take one ball from the third bag. We define the following random variables, for i = 1, 2, 3:  Xi =1 if the ball drawn from the i-th bag is white,   0 otherwise

(a) Show that P(Xi = 1) = a/(a+b) for i = 1, 2, 3.

(b) Let W be the random variable that represents the total number of white balls obtained out of the three draws (one from each bag). Use the result from part (a) to find E(W).