Note:

• The questions below are samples of the types of questions that will appear on Test #2 of I201/C251.
• It is doubtful that all these questions could be answered within one class’s worth of time, therefore, expect some subset of the questions that appear below.

1. Draw a tree diagram to show all the possible ways of answering a 3 question True/False quiz, starting with question #1.
2. Product Rule: How many license plates can be made with 3 letters and followed by 3 digits?
3. Sum Rule: How many letters can be made using 5 different character fonts?
4. Rule of Inclusion-Exclusion: How many 8-bit strings start with 00 and end with 11?
5. What principle should be used to answer the following question: “If there are 50 people in a room, then there is at least one month that has more than one person born in that month.  What is the minimum number of people in the room born in that month?”
   Use that principle to solve the “50 people in a room” question, above.
6. Of the following, which are “combination” problems, and which are “permutation” problems:
1. How many ways are there to select the 1^st, 2^nd, 3^rd, and 4^th places from a field of 25 contestants?
2. Five people arrive at a Coke machine to purchase a drink, how many different ways might those five people arrive at the machine?
3. How many hands of five cards can be dealt from a regular deck of cards?
7. Apply based on your answer to 15 a – 15 c (above) apply C(n, r) or P(n, r) to come up with the actual number that answers the questions asked.
8. With respect to combinations and permutations, when does order not matter and when does it not matter? Give examples of each.
9. In mathematical probability, what do the following mean: Experiment; Sample Space; Successful Outcomes; p(E), where E = the set of successful outcomes; p(s) where s S.
10. What is the probability that a card selected from a deck of cards is a King or a Spade?
11. In probability what is the result of evaluating the following: p(s)
12. In probability what is the meaning of the following: uniform distribution?, a fair experiment, a biased experiment, an equally likely outcome.
13. In probability, what is the formula for evaluating the following: p(E | F)?

14. To the right is a diagram of a function. a. What is the domain of the function? b. What is the range of the function? c. In probability this function has a special name, what is it? d. What is the probability distribution for this function?

15. What is the formula for the Expectation of a random variable?
16. What is the E(X) for the random variable in #14.
17. Conditional probability: What is the probability of flipping 3 heads given that the first of 3 flips is a head?
18. 4% of computers are infected with the NasTeaSmell virus.
    97% of infected computers test positive when scanned for viruses.
    2% of computers not infected test positive when scanned for viruses.
    What is the probability a computer testing positive is infected?
19. Find a₃ term of: a_n = a_n-1 + a_n-2, a₁ = 3, a₀ =4
20. Show that {a_n} is a solution to a_n = -4a_n-1 + 5a_n-2 if a_n = 1
21. Find a solution for the recurrence relation: a_n = 3a_n-1
22. Exercise 3, page 527.
23. Exercise 5, page 536.
24. Exercise 11, page 536.
25. Exercise 17, page 536.
26. Exercise 19, page 536.
27. Exercise 1, page 542.
28. Exercise 3, page 542.
29. Exercise 21, page 543.
30. Exercise 1, page 553.
31. Exercise 25, page 554.