(Hint for Question 2 attached below:

In question 2, first try to find P(Wi) and P(Bi) i.e. probabilities that i-th picked ball is white / black.

Using that you can construct decision three and with some algebra construct an expression.

Full credit will also be given if you define an iterrative expressions:

P(Wi|Bi-1) , P(Wi|Wi-1) , P(Bi|Wi-1), P(Bi|Bi-1), P(Wi-1), P(Bi-1)

so that it can be calculated for all i.)

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