Expected Value #sheldon and ross

Question

If n balls are randomly selected from an urn containing N balls of which m are white,find the expected number of white balls selected.

Answer 1

This is an example of hypergeometric distribution. Where we have n trials.probability of a ball being white = m/N since N is total no of balls

We know expectation no = np where n is no of trials and P is probability of success.

Hence expectation = n*m/N

Comments

@habibkhan , Is it same as your's or it is wrong-

E =$ \frac{ 1 * C(m,1) * C(N-m, n-1))}{C(N,n)}+ \frac{ 2 * C(m,2) * C(N-m, n-2))}{C(N,n)}$

$+ \frac{ 3 * C(m,3) * C(N-m, n-3))}{C(N,n)} + \frac{ 4 * C(m,4) * C(N-m, n-4))}{C(N,n)} + .....$

$+ \frac{ m * C(m,m) * C(N-m, 0))}{C(N,n)}$.

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It should be same

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The answered method was there in sheldon