E12 {20 points}: There are N boxes on the table each containing n1 white and n black balls. Assume you pick randomly one ball from the first box and put it in the second box. Then you pick randomly a ball from the second box and put it in the third box. The process is repeated until you pick randomly a ball from the last, the N-th box. a} Find probability that the third ball you pick is white if the first picked is black. b] Find probability that the last ball you pick is white if the first picked ball is black