Consider the box of red and blue balls in Examples 4.2.4 and 4.2.5. Suppose that we sample

Question:

Consider the box of red and blue balls in Examples 4.2.4 and 4.2.5. Suppose that we sample n > 1 balls with replacement, and let X be the number of red balls in the sample. Then we sample n balls without replacement, and we let Y be the number of red balls in the sample. Prove that Pr(X = n) > Pr(Y = n).