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January 5, 2019
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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) 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?

Step-by-step solution
  1. Step 1 of 2

    (a)

    The expected value of a lottery ticket is,

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  2. Step 2 of 2

    (b)

    The amount of the proprietor of the lottery needs to

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