An urn contains $N$ balls out of which $R$ are red and $B$ are blue. We picked randomly $10$ balls. Find the the expecting average of red balls.

Question

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An urn contains $N$ balls out of which $R$ are red and $B$ are blue. After picking randomly $10$ balls, find the formula for the expecting average of red balls.

Answer 1

Hint: Distribute the 10 balls you picked randomly among ten numbered bins, one ball in each. Then compute the expected number of red balls in bin 1, plus the expected number or red balls in bin 2, et cetera, plus the expected number of red balls in bin 10.

Answer 2

Hint.

Recall that if $I$ is an indicator random variable, then $$E[I] = P(I = 1).$$ Let $I_j$ for $j =1,\dotsc, 10$ denote the event that the $j$th ball drawn is red. Then $$N = I_1+\dotsb+I_{10}$$ denotes the number of reds.