## Discrete Probability

 General Information Syllabus Homework Assignments Exam Related

Homework assignments

Practice problems are not to be submitted, but are very important. You are encouraged to do even more of these than are assigned. Please use the solutions to odd numbered exercises or solutions provided in class to be sure that you understand these problems thoroughly.

Written assignments will be submitted in class. These will emphasize proofs, and must conform to the following proof-writing standards.

Week of Nov 29 -- Dec 3, 2004

 Wednesday, November 17: Read TBA. Practice problems  (for next class period) TBA. Written assignment  (for Wednesday, December 1) TBA.
 Monday, November 29: Read TBA Practice problems  (for next class period) TBA. Written assignment  (for Monday, November 29) TBA.

"Week" of Nov 22 -- Nov 22, 2004

 Monday, November 22: Read 11.3. Practice problems  (for next class period) 11.3: 3, 6. Written assignment  (for Wednesday, December 1) 11.3: 10, 13, 17.

Week of Nov 15 -- Nov 19, 2004

 Friday, November 19: Read 11.3. Practice problems  (for next class period) 11.3: 1, 5. Written assignment  (for Wednesday, December 1) 11.3: 2, 8, 15.
 Wednesday, November 17: Read 11.2. Practice problems  (for next class period) 11.2: 8. Written assignment  (for Friday, November 19) 11.2: 9, 19.
 Monday, November 15: Read 11.2. Practice problems  (for next class period) 11.2: 1, 3, 4. Written assignment  (for Friday, November 19) 11.2: 6, 15, 18. Additional problem: Suppose X has a Poisson distribution with parameter 11.5. Use Poisson probability tables to estimate P(X < 16), P(X > 8), and P(X = 14)

Week of Nov 8 -- Nov 12, 2004

 Friday, November 12: Read 11.1. Practice problems  (for next class period) 11.1: 2, 4, 7, 8. Written assignment  (for Friday, November 19) 11.1: 11, 12, 19. 9.2: 2.
 Wednesday, November 10: Read 11.1. Practice problems  (for next class period) None. Written assignment  (for Friday, November 19) None.
 Monday, November 8: Read 9.2. Practice problems  (for next class period) 9.2: 1, 7. Written assignment  (for Friday, November 12) 9.2: 5, 11.

Week of Nov 1 -- Nov 5, 2004

 Friday, November 5: Read 9.1, 9.2. Practice problems  (for next class period) 9.1: 5, 7, 8. Written assignment  (for Friday, November 12) 9.1: 12, 13, 17.
 Wednesday, November 3: Read 9.1, 9.2. Practice problems  (for next class period) 9.1: 1, 3, 4. Written assignment  (for Friday, November 12) 9.1: 6, 9, 10.
 Monday, November 1: Read 9.1, class notes. Practice problems  (for next class period) 5.2: 14, 25. Written assignment  (for Friday, November 5) 5.2: 26, 27, 28.

Week of Oct 25 -- Oct 29, 2004

 Friday, October 29: No class Submit homework to envelope outside of 412 Bradley by noon.
 Thursday, October 28: Read 8.1. Practice problems  (for next class period) 8.1: 1, 5, 6. Written assignment  (for Friday, November 5) 8.1: 9, 10. (8.1: 12 for extra credit) Additional problem: A city has 60,000 residents, 10,000 of whom are aged between 30 and 40. Suppose 10 residents are chosen at random. Write a precise formula for the probability that exactly 8 of these residents are aged between 30 and 40. (Do not evaluate this formula.) Write and evaluate a formula which approximates this probability by using a binomial model.
 Wednesday, October 27: Read 5.1, 8.1 Practice problems  (for next class period) 5.1: 14, 21, 26. Written assignment  (for Friday, November 5) 5.1: 27, 28, 32. Additional problem: A biased coin with P(H) = .3 is flipped 25 times. Let X be the number of heads. Use binomial probability tables to estimate P(X < 16), P(X > 8), and P(X = 14) to three significant digits.
 Monday, October 25: Read 5.1. Practice problems  (for next class period) 5.1: 35, 38. Written assignment  (for Friday, October 29) 5.1: 40, 42. (5.1: 43 for extra credit) Additional problem: A point is chosen at random from the region bounded by the curve y = 6x - 6x2 and the x-axis. What is the probability that the x-coordinate of this point is less than or equal to 1/4?

Week of Oct 18 -- Oct 22, 2004

 Friday, October 22: Read 5.1. Practice problems  (for next class period) 5.1: 6, 7. Written assignment  (for Friday, October 29) 5.1. 8, 9, 10. Additional problem: Professor Snell has published the following assertions concerning a random number X between 1 and 30. P ( X is odd ) = 1/2. P ( 15 < X < 20 ) = 2/15. P ( X is divisible by 10 ) = 1/10. In a competing study, Professor Skandera asked 30 students to choose random numbers between 1 and 30, and concluded the following. P ( X is odd ) = 7/10. P ( 15 < X < 20 ) = 1/3. P ( X is divisible by 10 ) = 0. Compare Skandera's results to those of Snell. What, if anything, might Skandera's results be measuring? (A possible interpretation.)
 Wednesday, October 20: Read 5.1. Practice problems  (for next class period) 5.1: 1, 2.
 Monday, October 18: Read 6.2. Review All sections so far for exam on Wednesday, October 20. Practice problems  (for Friday, October 22) 6.2: 2, 8, 10. Written assignment  (for Friday, October 22) 6.2: 15. Additional problem: A rat is placed in a maze. From its initial position it will move to the right or to the left, each with probability 1/2. If it moves to the right, then it will wander around the maze for 3 minutes and return to its initial position. If it moves to the left, then with probability 1/3 it will exit the maze in two minutes and with probability 2/3 it will wander around for 5 minutes and return to its inital position. Each time the rat returns to its initial position, it will move right or left, each with probability 1/2. What is the expected number of minutes required for the rat to exit the maze?

Week of Oct 11 -- Oct 15, 2004

 Friday, October 15: Read 6.2. Review All sections so far for exam on Wednesday, October 20. Practice problems  (for next class period) 6.2: 3. Written assignment  (for Friday, October 22) 6.2: 5, 9, 11, 12.
 Wednesday, October 13: Read 6.1, 6.2. Practice problems  (for next class period) 6.2: 4. Additional problems: (a) Two hats each contain four pieces of paper numbered 1, 2, 3, 4. One number is randomly drawn from each hat. What is the expected sum of the numbers? (Ans: 5.) (b) Given that neither of the drawn numbers is 3, what is the expected sum of the numbers? (Ans: 14/3.) Written assignment  (for Friday, October 15) 6.1: 36.
 Monday, October 11: Read 6.1. Practice problems  (for next class period) 6.1: 5, 6, 8. Written assignment  (for Friday, October 15) 4.1: 12, 18, 39. 6.1: 13, 14, 17.

Week of Oct 4 -- Oct 8, 2004

 Friday, October 8: Read 4.1, 6.1. Practice problems  (for next class period) 4.1: 13, 26, 29. Written assignment  (for Friday, October 15) 4.1: 27, 34, 36, 46.
 Wednesday, October 6: Read 4.1. Practice problems  (for next class period) 4.1: 5, 9. Written assignment  (for Friday, October 8) Additional problem: Alice, Bob, and n-2 other people are boarding an airplane with n seats. Alice, who has lost her boarding pass, is first in line and Bob is last. Alice chooses a seat at random. Each passenger behind her, including Bob, sits in his or her assigned seat if it is not occupied and chooses a seat at random if it is. For n = 2, 3, 4 find the probability that Bob sits in his own seat. Written assignment  (for Friday, October 15) 4.1: 8, 17, 22.
 Monday, October 4: Read 3.2, 4.1. Practice problems  (for next class period) 3.2: 23. 4.1: 3. Written assignment  (for Friday, October 8) 3.2: 22, 24, 34a.

Week of Sept 27 -- Oct 1, 2004

 Friday, October 1: Read 3.2. Practice problems  (for next class period) 3.2: 9, 11, 15. Written assignment  (for Friday, October 8) 3.2: 8, 20, 31.
 Wednesday, September 29: Read 3.2. Practice problems  (for next class period) 3.2: 1, 3. Written assignment  (for Friday, October 1) 3.1: 14, 23. 3.2: 12.
 Monday, September 27: Read 3.1. Practice problems  (for next class period) 3.1: 3, 5, 11. Written assignment  (for Friday, October 1) 3.1: 10, 12, 13, 17. Additional problem: Consider the warning, "Consuming raw or undercooked eggs may increase your risk of foodborne illness." Interpret the use of the words may and risk in terms of probability based upon opinions of certain people. What, if anything, does the warning mean? (Possible interpretations.)

Week of Sept 20 -- Sept 24, 2004

 Friday, September 24: Read 1.2, 3.1. Practice problems  (for next class period) 1.2: 10, 11, 13. Written assignment  (for Friday, October 1) 1.2: 22, 23, 31.
 Wednesday, September 22: Read 1.2. Practice problems  (for next class period) 1.2: 2, 6, 9. Written assignment  (for Friday, Oct. 1) 1.2: 16, 18, 25.