Lial 9th Edition
FM Dept Review P2 F09
Finite Math Departmental Review Part 2: 7.1 – 9.4
Directions:
1.
2.
Show all of your work on every problem.
Let D = {10, 13, 15}, E= {10, 12, 13, 14} and F = {9, 11, 12, 13, 15}. List the elements in the set
(D U E) ∩ F.
7.1.39
Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, A = {0, 2, 4, 6}, B = {0, 2, 4, 6, 8},
C = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Use A, B, and C to find the following: (A' U B) ∩ C.
7.1.40
3.
Arturo, Beau, Chloe, and Dean are four senators on a certain subcommittee. Any or none of them may be
selected to another subcommittee. How many different variations for the new subcommittee are there?
7.1.65
4.
Given the Venn Diagram below, shade the appropriate areas for:
a.
P∩Q
5.
Use the union rule to answer the question.
b.
P ∩ Q'
c.
(P ∩ Q)'
d.
(P ∩ Q) U (P ∩ R)
7.2.11
7.2.23
If n(A ∩ B) = 5, n(A U B) = 46, and n(A) = 30, what is n(B)?
6.
a.
A college survey was taken to determine where students study. Of 138 students surveyed, 84 studied in
the cafeteria, 75 studied in the student union, 34 studied in both the cafeteria and the student union.
Draw a Venn diagram to represent this information and use your Venn diagram to answer the following:
7.2.39
Of those interviewed how many studied only in the cafeteria?
b.
Of those interviewed how many studied only in the student union?
c.
Of those interviewed how many did not study in either the cafeteria or the student union?
7.
A survey of magazine subscribers placed 65 celebrities in 3 categories. 41 were on the most powerful list.
32 were on the most liked list. 26 were on the most intelligent list. 6 were on all three lists. 19 were on the
most powerful and most liked lists. 16 were on the most powerful and most intelligent lists. 10 were on the
most liked and most intelligent lists. Draw a Venn diagram and use it to answer the questions.
7.2.59
a.
How many were only on the most liked list?
b.
How many were on exactly one list?
c.
How many were on at least one list?
d.
How m any were on exactly two lists?
e.
How many were on none of the lists?
8.
A single fair die is tossed. Find the probability of rolling a number greater than 5.
9.
Suppose you draw a card from a well-shuffled deck of 52 cards. Find each of the following probabilities.
Write your answer as a simplified fraction.
7.3.25
a.
What is the probability of drawing a 6?
b.
What is the probability of drawing a black card?
c.
What is the probability of drawing a black 5?
7.3.21
1
Lial 9th Edition
FM Dept Review P2 F09
10.
Suppose you draw a card from a well-shuffled deck of 52 cards. Find each of the following probabilities.
Write your answers as simplified fractions.
7.3.31
a.
What is the probability of drawing a 7 or a queen?
b.
What is the probability of drawing a club?
11.
A marble is selected at random from a jar containing 2 red marbles, 5 yellow marbles, and 6 green marbles.
Find the probability that it is the following. Write your answers as simplified fractions.
7.3.39
a.
The marble is not yellow
b.
The marble is either red or green
12.
A monk crossbred plants, which can have purple or white flowers, and obtained 518 plants with white
flowers and 235 plants with purple flowers. Find the empirical probability that a plant had each type of
flower. Write your answers as a decimal rounded to the nearest hundredth.
7.3.53
a.
The probability that a plant had white flowers is _________________________.
b.
The probability a plant had purple flowers is _________________________.
13.
A pair of dice is rolled. Find the probability of getting the following. Write your answers as simplified
fractions.
7.4.10
a.
A sum greater than 6
b.
A sum less than 10
14.
The odds against Nolan getting promoted are 1 : 5. Find the probability that Nolan gets promoted. Simplify
your answer and write it as a fraction or an integer.
7.4.33
15.
A survey of 100 people about their music gave the following information: 39 bought blues music; 21 were
professors who bought blues music, and 27 were professors. Find the following probabilities. Write your
answers as decimals rounded to the nearest hundredth.
7.4.70
a.
b.
c.
d.
The probability that a person is a professor who bought non-blues music
The probability that a person buys blues music or is a professor
The probability that someone is not a professor
The probability that someone is not a professor but a buyer of blues music
16.
If the odds in favor of Chris winning the election are 6 : 5, then what is the probability that:
a.
Chris wins. Write your answer as a simplified fraction.
b.
Chris does not win. Write your answer as a simplified fraction.
17.
Two cards are drawn without replacement from an ordinary deck; find the probability that the second is not
a king, given that the first is a king. Simplify your answer.
7.5.7
18.
Consider a political discussion group consisting of 8 Democrats, 6 republicans, and 2 Independents.
Suppose that two group members are randomly selected, in succession, to attend a political convention.
Find the probability of selecting two Independents. Write your answer as a simplified fraction.
7.5.13
19.
The table below shows the result of a restaurant survey.
Meals
Lunch
Dinner
Total
Service Good
12
28
40
Service Poor
28
16
44
7.4.73
7.5.33
Total
40
44
84
Find the probability that the service was good, given that the meal was lunch.
2
Lial 9th Edition
FM Dept Review P2 F09
20.
A bicycle factory runs two assembly lines, A and B. 97% of line A’s products pass inspection and 94% of
line B’s products pass inspection. 50% of the factory’s bikes come off assembly line B and the rest come
off line A. Find the probability that one of the factory’s bikes did not pass inspection and came off assembly
line B. Write your answer as a decimal.
7.5.41
21.
In 2002, 66.5% of men and 50.1% of women in a country were overweight. Given that 48.6% of adults are
men and 51.4% are women, find the probability that a randomly selected adult fits the following
descriptions.
7.5.61
a.
An overweight man
b.
Overweight
c.
Are the events that an adult is a man and that an adult is overweight independent? Explain.
22.
If it snows tomorrow, the probability is 0.7 that John will practice his trombone. If it does not snow
tomorrow, there is only a 0.5 chance that John will practice. Suppose the chance of snow tomorrow is 50%.
What is the probability that John will practice his trombone?
7.5.71
23.
Suppose 25% of the population is 63 or over, 27% of those 63 or over have loans, and 54% of those
under 63 have loans. Find the probabilities that a person fits into the following categories. Write your
answers as a decimal rounded to three decimal places.
7.5.77
a.
The probability that a person is 63 or over and has a loan is ____________________.
b.
The probability that a person has a loan is ____________________.
On problems 24 – 27, make sure to show your tree diagram.
24.
Suppose you have 3 jars with the following contents. Jar 1 has 1 white ball and 2 black balls. Jar 2 has 4
white balls and 1 black ball. Jar 3 has 1 white ball and 2 black balls. One jar is to be selected and then 1
ball is to be drawn from the selected jar. The probability of selecting the first, second, and third jars are 1/3,
1/2 , and 1/6 respectively. Find the probability the ball was drawn from Jar 2 given that the ball was white.
Write your answer as a simplified fraction.
7.6.7
25.
Of all the people applying for a certain job, 90% are qualified and 10% are not. The personnel manager
claims that she approves qualified people 90% of the time; she approves unqualified people 20% of the
time. Find the probability that a person is qualified if he or she was not approved by the manager. Write
your answer as a decimal rounded to 3 decimal places if necessary.
7.6.11
26.
A manufacturer obtains clock-radios from three different subcontractors: 40% from A, 10% from B, and
50% from C. The defective rates for these subcontractors are 1%, 4%, and 4% respectively. If a defective
clock-radio is returned by a customer, what is the probability that is came from:
7.6.21
a.
subcontractor A? Round your decimal answer to three places, if necessary.
b.
subcontractor B? Round your decimal answer to three places, if necessary.
c.
subcontractor C? Round your decimal answer to three places, if necessary.
27.
A new lie-detector test has been devised and must be tested before it is put into use. Three hundred
people are selected at random, and each person draws and keeps a card from a box of 300 cards. Half the
cards instruct the person to lie and the others instruct the person to tell the truth. Of those who lied, 80%
fail the new lie-detector test (that is the test indicated lying). Of those who told the truth, 4% failed the test.
7.6.29
What is the probability that a randomly chosen subject will have lied given that the subject failed the test.
Round your answer to 4 decimal places as necessary.
a.
b.
What is the probability that the subject will not have lied given that the subject failed the test? Round your
answer to 4 decimal places as necessary.
28.
A man has 8 shirts and 4 ties. How many different shirt and tie arrangements can he wear?
8.1.15
3
Lial 9th Edition
FM Dept Review P2 F09
29.
Sally has 4 red flags, 3 green flags, and 5 white flags. How many 12-flag signals can she run up a flag
pole?
8.1.23
30.
In an experiment on social interaction, 8 people will sit in 8 seats in a row. In how many ways can this be
done?
8.1.33
31.
In a horse race, how many different finishes among the first 3 places are possible if 15 horses are running?
(Exclude ties)
8.1.37
32.
How many different 6-letter “words” can be made:
a.
If the first letter must be E, W, or T and no letter may be repeated?
b.
If repeats are allowed (but the first letter is E, W, or T)?
c.
How many of the 6-letter words (starting with E, W, or T) with no repeats end in R?
33.
How many different numbers can be formed using 8 out of the 9 digits 1, 2, 3, …, 9 if the numbers:
a.
Are not repeated?
b.
Can be repeated?
c.
Are not repeated but must begin with the digit 2?
d.
Are not repeated but must begin with the digits 21?
34.
How many different committees can be formed from 7 teachers and 33 students if the committee consists of
4 teachers and 3 students?
8.2.17
35.
A bag of 10 apples contains 3 rotten apples and 7 good apples. A shopper selects a sample of 3 apples
from the bag.
8.2.22
a.
How many different samples are possible?
b.
How many samples contain all good apples?
c.
How many samples contain at least 1 rotten apple?
36.
A group of 18 workers decides to send a delegation of 4 to their supervisor to discuss their work
assignments. In the following cases, determine the possible number of delegations.
8.1.42
8.1.43
8.2.30
a.
The number of 4 person delegations is ____________________.
b.
If the foreman must be included, the number of delegations is ____________________.
c.
If there are 7 women and 11 men in the group, then the number of delegations including exactly
one woman is ____________________.
37.
Jeanine Baker makes floral arrangements. She has 17 different cut flowers and plans to use 7 of them.
How different selections of the 7 flowers are possible?
8.2.43
38.
A bag contains 6 red balls and 6 blue balls. 2 balls are selected at random. Find the probability of selecting
2 red balls.
8.3.1
39.
If you are dealt 3 cards from a shuffled deck of 52 cards, find the probability that all 3 cards are queens.
8.3.6
40.
A shipment of 9 typewriters contains 4 that are defective. Find the probability that a sample of size 3, drawn
from the 9, will not contain a defective typewriter.
8.3.31
41.
What is the probability of winning a lottery in which you must choose 4 numbers from the numbers
1 through 17?
8.3.38
4
Lial 9th Edition
FM Dept Review P2 F09
42.
A bridge hand is made up of 13 cards from a deck of 52. Find the probability that a hand chosen at random
contains at least 2 twos.
8.3.47
43.
Assume the probability is ½ that a child born is a girl. If a family has three children, what is the probability
that they have:
8.4.1
a.
exactly one girl?
b.
at most two boys?
44.
A survey finds customers overpay for 2 out of every 20 items. Suppose a customer purchases 10 items.
8.4.25
a.
Find the probability the customer overpays on all of the items. Simplify your answer and write it as a
decimal rounded to the nearest thousandth.
b.
Find the probability the customer overpays on at most 2 items. Simplify your answer and write it as a
decimal rounded to the nearest thousandth.
45.
A student guesses on every question of a multiple-choice test that has 6 questions, each with 5 possible
answers. What is the probability that the student will get at least 4 of the questions right? Round to
4 decimal places as needed.
8.4.35
46.
According to an airline, a particular flight is on time 90% of the time. Suppose 37 flights are randomly
selected and the number of on time flights is recorded. Find the probabilities of the following events
occurring. Round your answers to 4 decimal places as needed.
8.4.40
a.
The probability that all 36 flights are on time is ____________________.
b.
The probability that between 31 and 33 flights, inclusive, are on time is ____________________.
47.
The probability that a male will be color-blind is 0.035. Find the probabilities that in a group of 58 men, the
following will be true. Round your answers to 4 decimal places as needed.
8.4.51
a.
Exactly 5 are color-blind
b.
No more than 5 are color-blind
c.
At least 1 is color-blind
48.
When treated with an antibiotic, 96% of all the dolphins are cured of an ear infection. If 7 dolphins are
treated, find the probability that exactly 4 are cured. Round your answer to 4 decimal places.
8.4.59
49.
A committee of 3 members is selected from a club made up of 11 junior members and 19 senior members.
What is the expected number of juniors in the committee? Round your answer to the nearest hundredth, if
necessary.
8.5.24
50.
A raffle offers a first prize of $1000, 2 second prizes of $300, and 20 third prizes of $10 each. If 8000 raffle
tickets are sold at 50 cents each, find the expected winnings for a person buying 1 ticket.
8.5.45
51.
The table below contains the salaries of the employees at the Raggs, Ltd. Clothing Store. What is the
mean, median, and mode salary?
9.1.36
Number
1
5
3
1
52.
Type
Owner
Salesperson
Secretary
Custodian
Salary
$29,300
$19,500
$16,400
$11,000
For the following set of numbers, find the mean.
9.1.11
12.6, 14.6, 25.6, 10.6, 25.6, 15.6, 11.6
5
Lial 9th Edition
FM Dept Review P2 F09
53.
For the following set of numbers, find the median. 14, 16, 27, 12, 27, 17, 13
9.1.15
54.
For the following set of numbers, find the mode. 67, 69, 67, 75, 69, 64, 71
If there is more than one mode, use a comma to separate the numbers. If there is no mode, write N for
your answer.
9.1.25
55.
An assembly-line machine turns out washers with the following thicknesses (in millimeters). Find the mean
and standard deviation of the thicknesses. Round your answers for the mean to 4 decimal places. Use that
answer to find the standard deviation rounded to four decimal places.
9.2.27
1.65, 1.21, 1.37, 1.93, 1.86, 1.38, 1.69, 1.56, 1.22, 1.77, 1.28, 1.98, 1.99, 1.96, 1.42, 1.71
56.
Suppose that the life expectancy of a certain brand of non-defective light bulbs is normally distributed, with
a mean life of 1300 hours and a standard deviation of 50 hours. If 90,000 of these bulbs are produced, how
many can be expected to last less than 1365 hours?
9.3.23
57.
An “average” jar of peanut butter contains 442 g with a standard deviation of 10.2g. Find the probability that
a jar contains less than 430 g. Assume a normal distribution. Round your answer to four decimal places as
needed.
9.3.40
58.
Suppose that 1000 coins are tossed. Find the probability of getting exactly 505 heads. Use the normal
curve approximation to the binomial distribution.
9.4.7
59.
The probability that a part produced by a certain factory’s assembly line will be defective is 0.025. Suppose
a sample of 130 parts is taken. Find the following probabilities by using the normal curve approximation to
the binomial distribution.
9.4.17
a.
Exactly 5 defectives
b.
No defectives
c.
At least 1 defective
6