When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear, and each headlight is checked to see whether it is properly aimed. Let X denote the number of headlights that need adjustment, and let Y denote the number of defective tires.

a. If X and Y are independent with pX(0)
.5, pX(1)
.3, pX(2)
.2, and pY(0)
.6, pY(1)
.1, pY(2)
pY(3)

.05, pY(4)
.2, display the joint pmf of (X, Y) in a joint probability table.

b. Compute P(X  1 and Y  1) from the joint probability table, and verify that it equals the product P(X  1)

P(Y  1).

c. What is P(X Y
0) (the probability of no violations)?

d. Compute P(X Y  1).