1. 1 Section 4.5 Miscellaneous Simulations

2. 4.5 Miscellaneous Simulations 2 “Left Turn Frustration” You can make a left turn out of campus by Bates House if there is no car coming in either direction. The chances that a car is coming from the left is 2/3. The chances that a car is coming from the right is 1/2. What are the chances that you can make a left turn without delay?

3. 4.5 Miscellaneous Simulations 3 1. Name of Problem:. 2. Outcomes whose Random integer probabilities we know: correspondences: 3. RandInt(,, ) 4. ( Trials): 5. Answer: Vote

4. 4.5 Miscellaneous Simulations 4 “Zork” Is Zork more likely to land in room A or B? Zork begins at “Start” and makes its way toward rooms A and B randomly selecting a path at each fork Animation

5. 4.5 Miscellaneous Simulations 5 1. Name of Problem:. 2. Outcomes whose Random integer probabilities we know: correspondences: 3. RandInt(,, ) 4. ( Trials): 5. Answer: “Mathematical” Answer Vote

6. 4.5 Miscellaneous Simulations 6 “Baseball World Series”World A is playing B. The first team to win 4 games wins the series. Team A has won the first game. Here are some ways the Series could end: Suppose that team A and team B each have a 50% chance of winning any single game What are the chances that A will win the series?

7. 4.5 Miscellaneous Simulations 7 1. Name of Problem:. 2. Outcomes whose Random integer probabilities we know: correspondences: 3. RandInt(,, ) 4. ( Trials): 5. Answer: Vote

8. 4.5 Miscellaneous Simulations 8 “Troll Epidemic” A disease strikes an island where 6 trolls live. The disease stays with a troll for 1 day. Then that troll becomes immune Troll #1 gets the disease on day 1. On day 2, while still infected, he randomly visits one of the other trolls. If the visited troll has not had the disease, it gets it and is infected for day 3. The visited troll then visits another troll on day 3 The disease is transmitted until an infectious troll visits an immune troll and the disease dies out. There is one troll visit per day. Trolls can’t visit themselves. Here are some examples Animation On average how many trolls will become infected?

9. 4.5 Miscellaneous Simulations 9 1. Name of Problem:. 2. Outcomes whose Random integer probabilities we know: correspondences: 3. RandInt(,, ) 4. ( Trials): 5. Answer: Vote

10. 4.5 Miscellaneous Simulations 10 “New Orleans Levees” To prevent New Orleans from being flooded certain levees must hold. For example: Mississippi River 1 2 3 5 New Orleans 6 4 There are 6 aging levees (1, 2, 3, 4, 5, 6) around New Orleans. The chances of any one levee failing during a hurricane are 50% Animation What are the chances that New Orleans will be flooded during the next hurricane?

11. 4.5 Miscellaneous Simulations 11 1. Name of Problem:. 2. Outcomes whose Random integer probabilities we know: correspondences: 3. RandInt(,, ) 4. ( Trials): 5. Answer: Vote

12. 4.5 Miscellaneous Simulations 12 “Hot Shooting in Basketball” Jamere has a 65% chance of making a basket every time she shoots in a basketball game. Last night she took 20 shots. After the game the coach was surprised to see that she made 6 shots in a row Should the coach have been surprised?

13. 4.5 Miscellaneous Simulations 13 1. Name of Problem:. 2. Outcomes whose Random integer probabilities we know: correspondences: 3. RandInt(,, ) 4. ( Trials): 5. Answer: Vote

14. 4.5 Miscellaneous Simulations 14 Alien Meeting Two aliens from a distant asteroid agree that both will come every night to the top of the Empire State Building between midnight and 1:00 a.m. The exact moment of each alien's arrival within that time span, however, is totally random. They further agree that each will vanish if the other has not appeared at the end of 10 minutes of if the stroke of 1 sounds. What are the chances that the aliens will meet?

15. 4.5 Miscellaneous Simulations 15 1. Name of Problem:. 2. Outcomes whose Random integer probabilities we know: correspondences: 3. RandInt(,, ) 4. ( Trials): 5. Answer: Vote

16. End of 4.5

17. 4.5 Miscellaneous Simulations 17 “Left Turn Frustration” — What's the best choice? 1.RandInt(1, 2, 2) 2.RandInt(1, 3, 2) 3.RandInt(1, 5, 2) 4.RandInt(1, 6, 2)

18. 4.5 Miscellaneous Simulations 18 “Zork” — What's the best choice? 1. RandInt(1, 2, 1) 2. RandInt(1, 2, 1) 3. RandInt(1, 3, 1) 4. RandInt(1, 3, 2) 5. RandInt(1, 6, 1) 6. RandInt(1, 6, 2)

19. 4.5 Miscellaneous Simulations 19 “Baseball World Series” — What's the best choice? 0 of 30 1. RandInt(1, 2, 6) 2. RandInt(1, 4, 6) 3. RandInt(1, 4, 7) 4. RandInt(1, 7, 1) 5. RandInt(1, 7, 4)

20. 4.5 Miscellaneous Simulations 20 “Troll Epidemic” — What's the best choice? 0 of 30 1. RandInt(1, 2, 1) 2. RandInt(1, 5, 1) 3. RandInt(1, 6, 1)

21. 4.5 Miscellaneous Simulations 21 “New Orleans Levees” — What's the best choice? 1. RandInt(1, 2, 6) 2. RandInt(1, 3, 6) 3. RandInt(1, 4, 6) 4. RandInt(1, 5, 6) 5. RandInt(1, 6, 6) 0 of 30

22. 4.5 Miscellaneous Simulations 22 “Hot Shooting in Basketball” What's the best choice? 0 of 30 1. RandInt(1, 5, 5) 2. RandInt(1, 10, 5) 3. RandInt(1, 20, 5) 4. RandInt(1, 100, 5)

23. 4.5 Miscellaneous Simulations 23 “Alien Meeting” — What's the best choice? 0 of 30 1. RandInt(1, 5, 5) 2. RandInt(1, 10, 5) 3. RandInt(1, 20, 5) 4. RandInt(1, 100, 5)

24. 4.5 Miscellaneous Simulations 24

25. Answer: Room B= L-L or S-R or R =(1/3)*(1/2) + (1/3)*(1/3) + 1/3 =1/6 + 1/9 + 1/3 = 3/18 + 2/18 + 6/18 =11/18 ~60%

26. 4.5 Miscellaneous Simulations 26 Healthy Infected Immune 3 were infected

27. 4.5 Miscellaneous Simulations 27 Healthy Infected Immune 4 were infected

28. 4.5 Miscellaneous Simulations 28 Healthy Infected Immune 2 were infected

29. 4.5 Miscellaneous Simulations 29 4 3 2 1 6 5 Levee before flood Levee failed Levee held

30. 4.5 Miscellaneous Simulations 30 Levee before flood Levee failed Levee held 4 3 2 1 6 5 1

31. Meta-Material