2. 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).