Chapter 15.3, Problem 13P

(a) A candy vending machine is out of order. The probability that you get a candy bar (with or without return of your money) is $\frac{1}{2},$ the probability that you get your money back (with or without candy) is $\frac{1}{3},$ and the probability that you get both the candy and your money back is $\frac{1}{12}.$ What is the probability that you get nothing at all? Suggestion: Sketch a geometric diagram similar to Figure 3.1, indicate regions representing the various possibilities and their probabilities; then set up a four-point sample space and the associated probabilities of the points.

(b) Suppose you try again to get a candy bar as in part (a). Set up the 16-point sample space corresponding to the possible results of your two attempts to buy a candy bar, and find the probability that you get two candy bars (and no money back); that you get no candy and lose your money both times; that you just get your money back both times.