In a lottery, 5000 tickets are sold for $1 each, one first prize of $2000, 1 second prize of $500, 3 third prizes of $100, and 10 consolation prizes of $25 are to be awarded. What are the expected net earnings of a person who buys one ticket?

Question

Kale Mccann

Mathematics

11 August, 17:29

In a lottery, 5000 tickets are sold for $1 each, one first prize of $2000, 1 second prize of $500, 3 third prizes of $100, and 10 consolation prizes of $25 are to be awarded. What are the expected net earnings of a person who buys one ticket?

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Paul Hurley · Answer 1

There is 1/5000 chance to win first place of $2000,

1/5000 chance to win second place of $500

3/5000 chance to win third place of $100

10/5000 chance to win the consolation prize of $25.

The ticket costs $1.

We multiply each probability by the amount, and subtract the ticket cost, to get the expected net earnings:

(1/5000) ($2000) + (1/5000) ($500) + (3/5000) ($100) + (10/5000) ($25) - $1 = $ (-0.39).

This means that there is an expected loss of $0.39.