Each day we randomly select a ball from an urn that initiall

Each day, we randomly select a ball from an urn that initially contains m black balls and n white balls. The selected ball will not be returned to the urn. If a black ball is chosen, we add a white ball into the urn.

(1) Let X denote the number of white balls in the urn after the last black ball has been chosen and the corresponding white ball has been put into the urn. Find E[X].

(2) Let Y denote the day on which the last black ball is chosen. Find E[Y ].

Solution

1)

E(X) will be (1-M) * n

2)

E(Y) will be M * N