1. The possible results of an experiment (rolling a die) are called its _______________________.

a) Eventsb) Outcomesc) Probabilityd) Combinations

2. _________________________ is often used to determine the expected results of an experiment or business venture over the long term.

a) Expected Valueb) Empirical Probabilityc) Guessworkd) Counting Principle

3. ________________________________ is the relative frequency of occurrence of an event and is determined by actual observations of an experiment.

a) Counting Principleb) Expected Valuec) Empirical Probabilityd) Law of Large #'s

4. In general, the probability of event E₂ occurring, given that an event E₁ has happened, is called a ___________________________________ and is written P (E₂ I E₁).

a) Conditional Probabilityb) Empirical Probabilityc)Theoretical Probabilityd) DeMorgan's Law

5. Events A and B are __________________________________ if it is impossible for both events to occur simultaneously.

a) Dependent Eventsb) Independent Events c) Certain Eventsd) Mutually Exclusive Events

Use the following information for questions 6-8. A veterinarian treats 18 dogs, 24 cats, 15 birds and 13 rabbits in a week. What is the empirical probability that the next animal she treats will...

6. be a doga) 9/35b) 35/9c) 12/35d) 3/14

7. not be a birda) 3/14b) 11/14c) 21/35d) 17/14

8. a cat or a rabbita) 39/70b) 21/35c) 37/70d) 12/35

For #9- 12, one card is selected at random from a deck of cards. Determine the probability of selecting each of the following.

9. a 7a) 1/52b)1/13c) 3/13d) 1/4

10. the 10 of clubsa) 1/52b)1/13c) 3/13d) 1/4

11. a diamonda) 1/52b)1/13c) 3/13d) 1/4

12. a picture carda) 1/52b)1/13c) 3/13d) 1/4

13. A person pays $25 to randomly select one of 5 envelopes containing a different check amount. Determine the expected value if the check amounts are $0, $20, $30, $35 and $75.

a) $135b) $7c) $32d) $13

There are 91 total days in the months of April, May and June. If two dates are selected at random from this time period, how many different outcomes are possible if the dates are selected.....

14. with replacementa) 182b) 8190c) 8281d) 273

15. without replacementa) 182b) 8190c) 8281d) 273

A hat contains 5 marbles: 1 red, 1 blue, 1 white, 1 green and 1 purple. Two marbles are to be selected (one at a time) out of the hat WITHOUT replacement. (12 pts)

16. Determine the number of points in the sample space using the counting principle.

a) 25b) 20c) 10d) 9

17. Construct a tree diagram and list each of the sample points in the sample space.

Determine the probability of selecting each of the following.

18. exactly 1 green marblea) 2/5b) 3/5c) 1d) 0

19. no blue marblesa) 2/5b) 3/5c) 1d) 0

20. two red marblesa) 2/5b) 3/5c) 1d) 0

Each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 is written on a separate piece of paper. One piece is randomly selected. Determine the probability of each of the following.

21. Selecting an even number or a number less than 5.

a) 5/6b) 2/3c) 7/12d) 3/4

22. Selecting a number less than 5 or a number greater than or equal to 9.

a) 5/6b) 2/3c) 7/12d) 3/4

Each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 is written on a separate piece of paper. 2 pieces are randomly selected (one at a time) WITHOUT replacement. Determine the probability of each of the following.

23. Selecting an Even number AND then an Even number

a) 3/11b) 1/4c) 11/23d) 5/22

A password for a website consists of 4 digits followed by 2 lowercase letters. Determine how many different passwords are possible if...

28. repetition of digits and letters is NOT allowed.

a) 6,760,000b) 3,276,000c) 200,000d) 6760

29. repetition of digits is permitted, and the letters must be 2 DIFFERENT vowels (a, e, i, o, u).

a) 6,760,000b) 3,276,000c) 200,000d) 6760

30. all 4 digits must be same, and the letters can be repeated.

a) 6,760,000b) 3,276,000c) 200,000d) 6760

31. Determine the number of permutations of the letters of the word: MISSISSIPPI

a) 69,300b) 34,650c) 17,325d) 138,600

Determine the number of ways each can occur.

32. Choosing 4 out of your 8 shirts for a vacation.

a) 1680b) 70c) 140d) 210

33. Choosing the 1^st place and 2^nd place winner of a horse race, comprised of 9 horses.

a) 36b) 1320c) 72d) 144

34. Choosing 4 appetizers out of the 11 choices on the dinner menu.

a) 7920b) 3960c) 660d) 330

35. Choosing a president, vice president and a secretary out of a group of 12 people.

a) 1320b) 220c) 660d) 132