The number of customers in line at a supermarket express checkout counter is a random variable whose probability mass function is given in the following table.

For each customer, the number of items to be purchased is a random variable with probability mass function.

Let X denote the number of customers in line, and let Y denote the total number of items purchased by all the customers in line. Assume the number of items purchased by one customer is independent of the number of items purchased by any other customer.

a. Find P(X = 2 and Y = 2).

b. Find P(X = 2 and Y = 6).

c. Find P(Y = 2).

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3 5 p(x) 0.10 0.25 0.30 0.20 0.10 0.05 3 4 5 2 p(y) 0.05 0.15 0.25 0.30 0.15 0.10