Question

A charity is holding a raffle to raise money. There is one car worth $30,000 and five $100 gift cards being raffled off. Each ticket costs $20, and there are a total of 5,000 tickets being sold. Which equation correctly depicts the calculation of the expected value for a ticket?

Answer 1

If 5000 tickets are sold, then the payout is $30,000 (really 29,980 because you paid $20 for the ticket) with probability 1/5000. Each of the five $100 gift cards ($80 after paying for the ticket) has probability 5/5000. Everyone else who buys a ticket loses $20 with probability 4994/5000. All of the probabilities have to sum to one.
The expected value of the winnings when you buy a ticket is
E(X) = $29980(1/5000) + $80(5/5000) + (-$20)(4994/5000) = $13.90

So if you spend $20 on a ticket, in the long run, if you play over and over, you win on average $13.90.

Winnings (X) P(X)
$29980 0.0002
$80 0.001
-$20 0.9988