Question

Lottery: I buy one of 400 raffle tickets for $20. The sponsors then randomly select 1 grand prize worth $500, then 2 second prizes worth $300 each, and then 10 third prizes worth $100 each. The selections are made without replacement.(a) Complete the probability distribution for this raffle. Give your probabilities as a decimal (rounded to 4 decimal places) or as a fraction.

Outcomes	P(x)
Win Grand Prize	?
Win a Second Prize	?
Win a Third Prize	?
Win Nothing	?

(b) Recognizing that I spent $20 to buy a ticket, determine the expected value of this raffle to me as a player. Round your answer to the nearest penny.
???????? dollars

(c) What is an accurate interpretation of this value?

It represents how much you would lose every time you play the game.

It represents the per-game average you would win/lose if you were to play this game many many times.

It is meaningless because you can't actually win or lose this amount.

It represents how much you would win every time you play the game

Answer 1

Probabilities are given by: Number of prizes for that stand / Total number of tickets

a. So P(X) is computed as:

Outcomes	P(x)
Win Grand Prize	1/400
Win a Second Prize	2/400 = 1/200
Win a Third Prize	10/400 = 1/40
Win Nothing	1 - (1+2+10)/400 =387/400 =0.967

b. Expected value of raffle = (1/400) * 500 + (1/200) * 300 + (1/50) * 100 - 20

(-20 as you paid for the raffle)

= -15.25

c. Correct interpretation:

It represents the per-game average you would win/lose if you were to play this game many many times.