If you find a winning ticket in your package, you win—on average— E($30,000/W) = $11,250). The expected value of the amount won is probably larger than you anticipated. We expect E(W) = 3 winners to share the prize, but the expected value E(30,000/W) is larger than 30,000/E(W) = 30,000/3 = $10,000.
People who play the carnival game Lucky Ducks pick a plastic duck from among those floating in a small pool. Each duck has a value written on the bottom that determines the prize. Most say “Sorry, try again!” Otherwise, 25% pay $1, 15% pay $5, and 5% pay $20. Let the random variable Y denote the winnings from picking a duck at random. ...