Socks in a drawer conundrum

A drawer contains 8 Red socks, 4 green socks and 4 yellow socks. Two socks

are chosen randomly from the drawer, without replacement. Let R be the number of red socks chosen and Y be the number of yellow socks chosen.

(a) Derive the joint probability mass function of R and Y , i.e. P(R = r, Y = y).

(b) Calculate the marginal probability distributions of R and Y , i.e. P(R = r) and P(Y = y), respectively.

(c) Are R and Y independent? Justify your answer.

(d) What is the probability that a pair of the same colour is chosen?

(e) Obtain the conditional distribution of R|Y = 1.

(f) Evaluate E[R], Var(R) and Cov(R, Y).