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 shows the probability mass function for the problem.
Table Probability model for Exercise 5.9.
$10 × 106
|Pr(X = xi,)||
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?
The expected value of a lottery ticket is,
The amount of the proprietor of the lottery needs to