1. Math Puzzles and Game Theory Final Exam Work through the slides, follow the directions, and fill in all required information.

2. SAVE YOUR WORK! It’s always a good idea to begin any electronic item by saving it. Save this file with the name: – “Math Puzzles FIRST NAME LAST NAME” – For example “Math Puzzles Jacob Bernoulli” Remember to repeatedly save throughout your time working on this.

3. Probability Answer the probability questions on the following slides by typing out decimal, fraction, or percent as each answer.

4. 1.P(1) = 1.P(even number) = 2.P(prime number) = 3.P(1 st spin is 2, 2 nd spin is 3) = 4.P(spin 1, 2, 3, 4, 5 in that order) =

5. Answer the following based off of drawing a single card from a standard 52-card deck. 6. P(king or a club) = 7. P(face card and red) = 8. P(red or club or spade) = 9. P(red club) =

6. Expected Value 10.A game consists of rolling a colored die with three red sides, two green sides, and one blue side. A roll of a red loses $2.00. A roll of green pays $2.00. A roll of blue pays $5.00. The charge to play the game is $2.00. Would you play the game? 11.Why or why not?

7. 12. Blackjack (Answer on next slide) Suppose you are playing Blackjack and you know the dealer has 16 and will have to take at least one more card: Which of the following hands would you prefer to have (you can hit and get more cards, or stay) and WHY? HAND A HAND B HAND C

8. 12. Blackjack answer

9. Roulette – The numbers on each chip represent how many dollars were wagered there. For example, $8 was placed on red. Determine the prizes awarded for each spin listed. 13. Black 10 = 14. Red 14 =

10. 15. Roulette Go to the website bit.ly/harenroulette by copying the link into Google Chrome.bit.ly/harenroulette Place a $500 bet on red and click Spin. Repeat this same bet 4 more times and record the 5 colors below. 1. 2. 3. 4. 5.

11. Roulette 16. You began the game with $5000. What did you end with? 17. Why do casinos have an advantage in roulette? When I bet on red shouldn’t I have a 50% chance of winning?

12. Tic-Tac-Toe 18. Is it possible to guarantee victory when you play tic-tac-toe? 19. Describe the best strategy for playing tic-tac-toe. Where should you start? What else?

13. 20. Go to the site: bit.ly/harentic Choose either Level 2 or Level 3 and play 10 games. When you are done, take a screenshot of your score by holding down the 4 buttons Command+Control+Shift+4 and then highlighting the area. Paste your screen shot below

14. Prisoner’s Dilemma You and your friend are members of a criminal gang and are arrested and imprisoned. Each of you is in solitary confinement with no means of speaking to or exchanging messages with the other. The prosecutors do not have enough evidence to convict each of you on the principal charge. Simultaneously, the prosecutors offer each of you a bargain. Each of you is given the opportunity either to: confess by testifying that the other committed the crime or remaining silent. Here is the offer: If you and your friend each confess, you each get 5 years in prison If you confess but your friend remains silent, you will be set free but your friend will serve 20 years (and vice versa) If you and your friend both remain silent, you will each only serve 1 year.

16. Prisoner’s Dilemma 21. If you and your best friend were in this scenario and you didn’t have time to create a plan, how would you handle the situation? Would you remain silent or betray your friend? Whatever decision you make, you must explain yourself by addressing all scenarios. E.g. if you pick silence, explain what would happen if your friend confessed or if your friend remained silent and why you are opting for that choice.

17. John Nash, famous for his works in game theory, died last year. Go to this link to read about him and answer questions on the following slide: bit.ly/harennash

18. Answer the following questions about the article: 22. What is defined as a situation in which each player employs an optimal strategy knowing the strategies of all other players? 23. According to the article what is a good strategy for kicking or saving penalty kicks in soccer? 24. Go to the John Nash wikipedia page: bit.ly/wikinash and state something interesting you find there in the space below.

19. 25. One game that John Nash worked on in regards to Game Theory is called Hex. Go to this site: bit.ly/harenhex and try to win a game. Regardless of whether you win or lose, take a screenshot of a completed game and paste it below.

20. The following questions will in no way affect your grade. Please answer honestly. Name some lessons, activities, stuff we did so far this year that you enjoyed. What do you like about how the class was run so far this year? What do you not like about how the class was run so far this year? Be honest and helpful. We have another semester together and would like to improve if possible. Any other comments?

21. You’re done! Airdrop your file to me or E-mail your file to my school e-mail: – charen@laca.org charen@laca.org Remember, your file should be named: – “Math Puzzles FIRST NAME LAST NAME”