I am not understanding the explanation here in regards to expectations and probabilities for sampling without replacement. I am not seeing why we don't treat each draw as a unique random variable. For example, if there is only one ball left, then Pr(Xn = red) can either only be 1 or 0. We don't know which one it is until we get there, but clearly Pr(Xn = red) does not equal p. (Let's assume originally we have 3 reds and 7 blues.)
The below excerpt implies that Pr(Xi = red) = p for all i. And thus, it implies Pr(Xn = red) = 0.30, not 1 or 0.