A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.

y
p(x, y)

0 1 2
x 0 0.10 0.03 0.01
1 0.08 0.20 0.06
2 0.05 0.14 0.33

(a) Given that X = 1, determine the conditional pmf of Y�i. e., pY|X(0|1), pY|X(1|1), pY|X(2|1). (Round your answers to four decimal places.)

y 0 1 2
pY|X(y|1)

(b) Given that two hoses are in use at the self-service island, what is the conditional pmf of the number of hoses in use on the full-service island? (Round your answers to four decimal places.)

y 0 1 2
pY|X(y|2)

(c) Use the result of part (b) to calculate the conditional probability
P(Y ? 1 | X = 2). (Round your answer to four decimal places.)
P(Y ? 1 | X = 2) =

(d) Given that two hoses are in use at the full-service island, what is the conditional pmf of the number in use at the self-service island? (Round your answers to four decimal places.)

x 0 1 2
pX|Y(x|2)