A certain market has both an express checkout line and a superexpress checkout line. Let X₁ denote the number of customers in line at the express checkout at a particular time of day, and let X₂ denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X₁ and X₂ is as given in the accompanying table.

	x2
		0	1	2	3
x1	0	0.08	0.07	0.04	0.00
1	0.05	0.15	0.05	0.04
2	0.05	0.04	0.10	0.06
3	0.01	0.03	0.04	0.07
4	0.00	0.02	0.05	0.05

(a) What is P(X₁ = 1, X₂ = 1), that is, the probability that there is exactly one customer in each line? P(X₁ = 1, X₂ = 1) = (b) What is P(X₁ = X₂), that is, the probability that the numbers of customers in the two lines are identical? P(X₁ = X₂) = (c) Let A denote the event that there are at least two more customers in one line than in the other line.

A = {X₁ 2 + X₂ X₂ 2 + X₁}

Calculate the probability of this event. P(A) = (d) What is the probability that the total number of customers in the two lines is exactly four? At least four?

P(exactly four)	=
P(at least four)	=