15.2. Expected Value and Payoffs http://www.ck12.org
- What is the payoff of a slot machine that costs 25 cents to play and pays out $1 with probability 10%, $50 with
probability of 1%, and $100 with probability 0.01%? - A slot machine pays out $1 with probability 5%, $100 with probability of 0.5%, and $1000 with probability
0.01%? If the casino wants to guarantee that they won’t lose money on this machine, how much should they charge
people to play? - What is the expected value of an experiment with the following outcomes and corresponding probabilities?
TABLE15.7:
Outcome 12 14 18 20 21 22 23
Probability 0.05 0.1 0.6 0.1 0.1 0.03 0.02Calculate the final grades for each of the students given the information in the table.
TABLE15.8:
Category Weight Sarah Jason Kimy Maria Kayla
Quizzes and
Tests30% 74% 85% 90% 80% 75%
Homework 25% 95% 40% 100% 90% 95%
Final 20% 68% 80% 85% 70% 50%
Projects 20% 85% 70% 95% 75% 85%
Participation 5% 95% 100% 100% 80% 60%- What is Sarah’s final grade?
- What is Jason’s final grade?
- What is Kimy’s final grade?
- What is Maria’s final grade?
- What is Kayla’s final grade?
- Look back at the grades and final grades for the five students. Do the grades seem fair to you given how each
student performed in each of the areas? Do you think the category weights should be changed? - You are in charge of a booth for a game at the fair. In the game, players pick a card at random from the deck.
If the card is a J, Q, or K, the player wins $5. What is the minimum amount you should charge in order to feel
confident you will make a profit by the end of the fair? - Make up your own game that has at least 2 possible outcomes with an expected payoff of $0.50.
- Explain why it makes sense for a casino to consider the concept of expected value when designing their games.