Expected number of red balls

Topic: Random variables and distributions · more questions on this topic
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Ten balls are drawn from an urn with 25 red balls and 75 white balls. Find the expected number of red balls in the draw. Does the answer change if the draw is without replacement rather than with replacement?

Worked answer (click to show)

With replacement the count is \operatorname{Bin}(10,1/4). Without replacement it is hypergeometric, 10 draws from 100 balls of which 25 are red. The distributions differ. The expectation is 10\times(25/100)=2.5 in both cases, by linearity applied to the ten indicator variables. Dependence changes the variance, not the mean.