An urn initially contains m black and n white balls At the b

An urn initially contains m black and n white balls. At the beginning of each day, we add k white balls and then randomly withdraw k balls from the balls in the urn. Let X denote the number of black balls at the end the day N. Find E[X].

Solution

total balls = m+n+k

total m black

total n+k white

probability of black = m/(m+n+k)

E(X) = K*P(B) = KM/(M+N+K)