Lottery. A lottery offers a grand prize of $10 million. The probability of winning this
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.
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) Fiftyfive million lottery tickets will be sold. How much does the proprietor of the lottery need to charge per ticket to make a profit?

Step 1 of 2 (a)
The expected value of a lottery ticket is,
Comment 
Step 2 of 2 (b)
The amount of the proprietor of the lottery needs to