Lottery stats Probability Distribution & expected value

Question

I buy one of 5000 raffle tickets for $1. The sponsors then randomly select one grand prize worth $500, two second prizes worth $200 each, and three third prizes at $100 each. Create the probability distribution for this raffle and calculate my expected value.

Answer 1

The probability distribution needs to list all possible outcomes and their probability. For this problem there are 4 outcomes (no prize:-1,1st:+499,2nd:+199,3rd:+99). The expected gain for each prize is 1 less because it cost $1 to buy the ticket. To find the probability of each of these outcomes, you need to look at how many tickets out of the total would earn each prize - There are 2 2nd prize winners, so the probability will be 2/5000. To find the expected value you will need to multiply each outcome by its probability and then add them all.