Question

In the lottery every week, 2,000,000 tickets are sold for $1 apiece. Say 4000 of these tickets pay off $30 each, 500 pay off $800 each, and one ticket pays off $1,200,000 and no ticket pays off more than one prize.
(a) What is the expected value of the winning amount for a player with a single ticket?
(b) What is the expected value of the winning amount for a player with five tickets?

Answer 1

The expected value is just the weighted average of how much one ticket wins. To calculate it, we need to find the probabilities of winning each dollar amount, multiply each probability with it's respective dollar amount, then find the sum.

Let's call the winnings from one ticket X:

P(X=30) = 4000/2000000 = 0.002

P(X=800) = 500/2000000 = 0.00025

P(X=1200000) = 1/2000000 = 0.0000005

E(X) = 30*P(X=30) + 800*P(X=800) + 1200000*P(X=1200000) = 0.06 + 0.2 + 0.6 = 0.86

The answer is $0.86