Two balls, one at a time, are drawn without replacement from a box containing r red and b black balls.

(a) For i = 1, 2, let X_i = 1 if the ith ball is red, and X_i = 0 otherwise. Do you expect negative or positive correlation between X₁ and X₂? Compute Corr{X₁,X₂}.

(b) Let Y₁ and Y₂ be the numbers of red and black balls in the sample, respectively. What is Corr{Y₁,Y₂}? (Advice: Try to avoid calculations.)