Expected Value · Example 3
In the casino game keno, a machine chooses at random 20 numbers between 1 and 80 (inclusive) without replacement. Players try to predict which numbers will be chosen. Players don’t try to guess all 20, though; generally, they’ll try to predict between 1 and 10 of the chosen numbers. The amount won depends on the number of guesses they made and the number of guesses that were correct.
(a) At one casino, a player can try to guess just 1 number. If that number is among the 20 selected, the player wins $2; otherwise, the player loses $1. What is the expected value?
(b) At the same casino, if a player makes 2 guesses and they’re both correct, the player wins $14; otherwise, the player loses $1. What is the expected value?
(c) Players can also make 3 guesses. If 2 of the 3 guesses are correct, the player wins $1. If all 3 guesses are correct, the player wins $42. Otherwise, the player loses $1. What is the expected value?
(d) Which of these games is the best for the player? Which is the best for the casino?
OpenStax, Contemporary Mathematics · §7.11 Expected Value · Example 3
No hints for this one.
Check your full solution
Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.
Your first check today doesn't need an account.
Your photos and PDFs are read once and not stored — only the transcription is kept.