Practice Quiz: Chapter 5 — TC3 MATH200 (Brown)

Work this like a regular quiz, using only your crib sheet. Give yourself a maximum of 23 minutes, then turn to the solutions and see how you did.

Remember, you must show your work for full credit on any problems involving computation.

Note: Many students have a lot of trouble with probability, so this quiz is extra long to help you practice.

1(points: 2) The DMV is planning a new issue of license plates using three letters (A–Z but no I, O, or Q) followed by some number of digits (0–9). No letter or digit can appear more than once on a given plate. How many digits must be used, in addition to three letters, to guarantee at least 20,000,000 unique license plates?

2(points: 3) You toss three coins.
(a) Construct the sample space of equally likely events.
(b) Find P(2H), the probability of getting exactly two heads.

3(points: 3) P(A), the probability of event A, is 0.7. A and B are complementary events.
(a) Find P(not A).
(b) Find P(B).
(c) Find P(A and B).
If any of the above cannot be determined from the information given, say so.

4(points: 3) A bag contains 1 molasses and 3 chocolate cookies. Reaching in without looking, you draw out two cookies. (a) Construct a sample space of equally likely events. (b) Find the probability that your two cookies are the same type.

5(points: 2) From either dice or cards, give an example of a pair of complementary events where the probabilities are not ½.

6(points: 4) You’ll be missing your favorite show while you’re in Statistics class. You set your Tivo, but just to be safe you also set your creaky old VCR to record it. But you’re having roommate trouble, and there’s a 20% chance your roommate will reprogram the Tivo. The VCR just unaccountably fails 30% of the time. What’s the probability that your program will be recorded?

	Male	Female	Total
	Registrations (thousands)
Democrat	21	28	49
Republican	24	21	45
Green	2	3	5
other	0	1	1
Total	47	53	100

Voter registrations in a fictional New York county are summarized in the table. Use the table to answer these questions about a randomly selected registered voter:

7(points: 2) P(Republican or Female) =

8(points: 2) P(Republican and Female) =

9(points: 2) P(Republican | Female) =

10(points: 3) Tom Turkey invested in two stocks, A and W. There is a 0.90 probability that company A will go bankrupt, and a 0.80 probability that company W will go bankrupt. Assuming the two companies have no connection, what is the probability that one of them, but not both, will go bankrupt?

11(points: 4) Without looking, Grace Underfire takes two sourballs from a bowl that contains 11 cherry and 9 orange flavor. What is the probability that she will get one of each flavor?

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Solutions to this practice quiz are available at http://www.tc3.edu/instruct/sbrown/stat/