STATISTICS - MATH 200

Question

For a fundraiser, 1000 raffle tickets are sold and the winner is chosen at random. There is only one prize, $500 cash. You buy one ticket.

a) what is the probability you will win $500

b) your expected earnings can be found by multiplying the value of the prize by the probability you will win the prize. What are your expected earnings?

c) if a ticket costs $2, what is the difference between your "costs" and expected earnings? How much are you effectively contributing to the fundraiser?

Please show work - I want to know HOW to do the problem not just the answer!

Answer 1

Chance of winning is 1/1000..or .1%

expected earnings - 1/1000 x 500= .50 or 50 cents.

$2 dollar ticket- .50 expected earnings yields an effective profit of 1.50 per ticket for the raffle.

Answer 2

a) Buying one ticket with 1000 total tickets being sold means your probability of winning is 1/1000.

b) Since expected earnings is defined as the probability you will win the prize multiplied by the value of the prize, it must be 1/1000 x 500 = $0.50

c) If a ticket costs $2, your cost is $2. Then the difference between your costs and your expected earnings is $2.00 - $0.50 = $1.50. That means every person who bought a ticket effectively donated $1.50. Another way of looking at this is the total revenue at $2 per ticket for 1000 tickets is $2000 and the total outlay on prizes is $500 so the total "take" for the raffle is $1500 and since there were 1000 tickets sold, each ticket donated $1.50