Solved: When an automobile is stopped by a roving safety

Chapter 5, Problem 4.138

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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).