# Northern Essex Community College, Quantitative Reasoning-MAT122-01A, Spring 2017: Exam #2

Questions:

1. There is a rack of 15 billiard balls. Balls numbered 1 through 8 are solid-colored. Balls numbered 9 through 15 contain stripes. If one ball is selected at random, determine the odds  against it being solidcolored.
2. A certain lottery requires players to select 4 different numbers, in any order, from 1 to 56 inclusive. How many different sets of 4 numbers can be chosen?
3. A controlled operation that yields a set of results is called a(n) _______.
4. A multiple-choice test has eight possible answers for each question.
(a) If a student guesses at the answer, what is the probability that he or she selects the correct answer for one particular question?
(b) If the student first eliminates one of the eight possible answers and guesses from the remaining possibilities, what is the probability that he or she selects the correct answer to that question?

5. Any ordered arrangement of a given set of objects is called a(n) ________.
6. Evaluate the expression.
$0!$
7. Probability determined by the relative frequency of occurrence of an event, or actual observations of an experiment is called _______ probability.
8. In an experiment, if there is neither a gain nor a loss in the long run, the expected value is _______.
9.  Probability problems that require obtaining a favorable outcome in each of the given events are ________ probability problems.
10. The manager at the local auto shop has found that the probability that a car brought into the shop requires an oil change is 0.81, the probability that a car brought into the shop requires brake repair is 0.19, and the probability that a car requires both an oil change and brake repair is 0.19. For a car brought into the shop, determine the probability that the car will require an oil change or brake repair.
11. Consider the figures to the right. Assume that one number from 1 to 7 is equally likely to be selected at random. Each number corresponds to one of the seven figures. Determine the probability of selecting an odd number, given that a
triangle is selected.
12. A television network, Network A, is scheduling its fall lineup of shows. For the Tuesday night 8 p.m. slot, Network A has selected its top show. If its rival network, Network B, schedules its top show during the same time slot, Network A estimates that it will get 1.4million viewers. However, if Network B schedules a different show during that time slot, Network A estimates that it will get 1.7 million viewers. Network A believes that the probability that Network B will air their top show is 0.3 and the probability that Network B will air another show is 0.7. Determine the expected number of viewers for Network A’s top show.
13. If the wheel is spun and each section is equally likely to stop under the pointer, determine the probability that the pointer lands on a even number, given that the color is red or gold.
14. A single fair die is rolled twice.
a) Determine the number of points in the sample space.
b) Construct a tree diagram and determine the sample space.
c) Determine the probability that a double (a 1, 1 or 2, 2, etc.) is rolled.
d) Determine the probability that a sum of 2 is rolled.
e) Determine the probability that a sum of 10 is rolled.
f) Are you as likely to roll a sum of 2 s you are of rolling a sum of 10?

15. A bag contains four batteries, all of which are the same size and are equally likely to be selected. Each battery is a different brand. If you select two batteries at random, use the counting principle to determine how many points will be in the sample space if the batteries are selected
a) with replacement.
b) without replacement.

16. Evaluate the expression
$\frac{_5C_3}{_{13}C_3}$
17. Select the correct choice that completes the sentence below.
The notation for the probability of E2, given E1, is _______.
18. A die is tossed. Find the odds against rolling a number greater than 3.
19. Evaluate the expression.

a. $_{20}C_0$
b.  $_{20}P_0$

20. Use the following statement to answer parts a) and b). One hundred raffle tickets are sold for $3 each. One prize of$200 is to be awarded. Winners do not have their ticket costs of \$3 refunded to them. Raul purchases one ticket.
a) Determine his expected value.
b) Determine the fair price of a ticket.

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