Lottery. A lottery offers a grand prize of $10 million. The probability of winning this grand prize is 1 in 55 million (≈1.8 × 10−8). There are no other prizes, so the probability of winning nothing = 1 − (1.8 ×

10−8) = 0.999999982. Table 5.5 shows the probability mass function for the problem.

TABLE 5.5 Probability model for Exercise 5.9.

Winnings

(X)

0 $10 × 106 Pr(X = xi

) 0.999999982 1.8

× 10−8

(a) What is the expected value of a lottery ticket?

(b) Fifty-five million lottery tickets will be sold. How much does the proprietor of the lottery need to charge per ticket to make a profit?