Question

Three thousand tickets are sold for $5 each. There is a $500

prize, a $250 prize, a $125 prize and a $50 prize. What is the
expected value for a person that buys a ticket? Round to the
nearest cent.

Answer 1

Answer: $0.31

Explanation:

1/3000 tickets will be worth $500.

1/3000 tickets will be worth $250.

1/3000 tickets will be worth $125.

1/3000 tickets will be worth $50.

The remaining 2996/3000 tickets will be worth $0. (Nobody else wins.)

So (1/3000)x500 + (1/3000)x250 + (1/3000)x125 + (1/3000)x50 + (2996/3000)x0 = $0.31.

Please note: This question asks for expected value. Expected value is a measure of what you should expect to get per game. The payoff of a game is the expected value of the game minus the cost.

Answer 2

Explanation:

The total amount of money collected from the ticket sales is:

$5/ticket x 3000 tickets = $15,000

The expected value for a person that buys a ticket can be calculated by adding up the probabilities of winning each prize multiplied by the amount of money for each prize:

E(X) = (1/3000) x $500 + (1/3000) x $250 + (1/3000) x $125 + (1/3000) x $50 - (2996/3000) x $5

Simplifying this expression:

E(X) = $0.1666667 + $0.0833333 + $0.0416667 + $0.0166667 - $4.9833333

E(X) = -$4.65

Therefore, the expected value for a person that buys a ticket is -$4.65, which means that on average, a person can expect to lose $4.65 for every ticket they buy.