CSN Math 104B
Applied Mathematics
Chapter 4:
Probability & Statistics
~ Exercises ~
Jim Matovina
Math Professor
College of Southern Nevada
[email protected]
Ronnie Yates
Math Professor
College of Southern Nevada
[email protected]
 Copyright 2011, 2012 - Jim Matovina, Ronnie Yates, All Rights Reserved
Section 4.1 Exercises
1. A club is to elect a president and a treasurer from the 30 members. How many ways can those
two officers be elected?
2. Sandra has 8 shirts and 5 pairs of pants. How many different outfits can she make?
3. Area codes are made up of 3-digit numbers.
a. If all numbers can be used for each digit, how many area codes are possible?
b. How many area codes would be possible if repetition is not allowed?
4. A school gymnasium has 6 different doors. How many ways can a person enter the gymnasium
and then leave through a different door?
5. A license plate consists of 2 letters followed by 3 numbers.
a. How many of these license plates are possible?
b. How many plates are possible if repetition is not allowed?
Evaluate:
6. 4!
10.
7P3
7. 7!
8. 11!
11. 5 P 5
9. 9!/5!
12. 5 P 1
13. 9 P 5
14. You have 8 books to place on a shelf, but you only have room for 4 of them. How many different
ways can you arrange books on this shelf?
15. Sam has 5 favorite football teams. Every week he puts their flags on his flagpole in random order.
a. How many different ways can he arrange the flags?
b. If he only has room for 3 of the flags on his flagpole, how many different ways can they be
arranged?
16. A baseball team is made up of 9 players. How many different batting orders are possible?
17. Ten runners are in a race. How many different ways can they finish in 1st, 2nd, and 3rd place?
Evaluate:
18. 7 C 4
19. 8 C 3
20. 5 C 5
21. 6 C 0
22. Of 6 students in a class, two will be chosen to go on a field trip. How many different ways can
they be selected?
23. Of the 12 players at an awards dinner, 3 of them will be given identical trophies. How many
different ways can the trophies be given out?
24. A teacher chooses 4 of her 12 students to help clean the room after school. In how many ways can
the students be chosen?
25. A student must answer 5 of the 8 essay questions that are on an exam. How many ways can the
student select 5 questions?
26. What is the difference between a permutation and a combination? Give an example of each.
Section 4.2 Exercises
For Exercises #1-11, a quarter is flipped and a single die is rolled.
1. Use the counting principle to determine the total number of outcomes.
2. List the sample space of all possible outcomes.
3. Find the probability of getting Heads and a 3.
4. Find the probability of getting Tails and a 7.
5. Find the probability of getting Heads and an odd number.
6. Find the probability of getting Heads and a number greater than 6.
7. Find the probability of getting Tails or a 7.
8. Find the probability of getting Tails or a number less than 9.
9. Find the odds of obtaining a Head.
10. Find the odds of obtaining a 6.
11. Find the odds of obtaining an even number.
For Exercises #12-16, a quarter is flipped and a penny is flipped.
12. Use the counting principle to determine the total number of outcomes.
13. List the sample space of all possible outcomes.
14. Find the probability of getting Tails on the quarter and Tails on the penny.
15. Find the probability of getting exactly one Tails.
16. Find the probability of getting no Tails.
For Exercises #17-21, the letters FRACTION are written on slips of paper and placed into a hat. Two
of these letters will be pulled out of the hat, without replacement, one after the other.
17. Use the counting principle to determine the total number of outcomes.
18. List the sample space of all possible outcomes.
19. Find the probability that the first letter is a vowel.
20. Find the probability that both letters are vowels.
21. Find the probability that neither letter is a vowel.
For Exercises #22-26, a pair of dice is rolled and the sum of the faces is obtained.
22. Find the probability that the sum is 5.
23. Find the probability that the sum is odd.
24. Find the probability that the sum is divisible by 3.
25. Find the odds against the sum being 11.
26. Find the odds against the sum being 5.
For Exercises #27-31, data regarding the transportation
of children to school is given in the table on the right.
Use the information in the table, find:
Boys
Girls
Bus
9
3
Car
5
8
27. The probability that a student chosen at random is a girl.
28. The probability that a student chosen at random rides the bus.
29. The probability that a student chosen at random rides in a car.
30. The probability that a student chosen at random is a girl who rides the bus.
31. The probability that a student chosen at random is a boy who rides in a car.
For Exercises #32-36, a bag of jellybeans contains 24 of them, with the colors as follows:
Red = 5, Blue = 3, Orange = 7, Green = 4, Yellow = 2, Purple = 3
32. Find the probability that a jellybean selected at random is orange.
33. Find the probability that a jellybean selected at random is green or yellow.
34. Find the probability that a jellybean selected at random is either red or purple.
35. Find the probability that a jellybean selected at random is anything but yellow.
36. Find the probability that a jellybean selected at random is black.
For Exercises #37-45, a single card is drawn from a standard deck of 52 cards
37. Find the probability that the card is the king of hearts.
38. Find the probability that the card is a nine.
39. Find the probability that the card is a red card.
40. Find the probability that the card is a red nine.
41. Find the probability that the card is a jack or a heart.
42. Find the probability that the card is an ace and a heart.
43. Find the probability that the card is a face card.
Section 4.3 Exercises
1. Given the spinner on the right:
a. Find the expected value.
b. What does this expected value
mean?
2. Given the spinner on the right:
a. Find the expected value.
b. What does this expected value
mean?
3. Five hundred tickets will be sold for a raffle, at a cost of $2 each. The prize for the winner is $600.
a. What is the expected value for playing this raffle?
b. What is a fair price to pay for a ticket?
4. Four baseball caps are on a table. One cap has a $1 bill under it, another has a $5 bill, another has
a $50 bill, and the last one has a $100 bill. You can select one cap, and keep the amount of money
that is underneath.
a. What is the expected value for playing this raffle?
b. Should you pay $45 to play?
5. An American roulette wheel contains slots with numbers from 1 through 36, and slots marked 0
and 00. Eighteen numbers are colored red and eighteen numbers are colored black. The 0 and 00
are colored green. You place a $1 bet on a roulette wheel betting that the result of the spin will be
green. If you win, the amount of your winnings is $17.
a. What is the expected value of this bet? Round your answer to the nearest hundredth.
b. What does this expected value mean?
c. The “Tower” is the display of the last ten to twenty winning numbers, and is often erected
next to the Roulette wheel. Should these numbers be used in determining your next bet? Why?
d. A European Roulette Wheel does not have the 00. How does this change the expected value?
6. Who said, “You cannot beat a roulette table unless you steal money from it.”
Section 4.4 Exercises
For Exercises #1-4, find the mean, median and mode of each data set. Round any decimal answers to
the nearest tenth.
1. {1, 3, 5, 5, 7, 8, 9, 11}
2. {5, 13, 8, 4, 7, 2, 11, 15, 3}
3. {37, 52, 84, 99, 73, 17}
4. {4, 16, 9, 4, 2, 4, 1}
5. During the month of November 2008, the Oakland Raiders played five football games. In those
games, the team scored the following number of points: 0, 6, 15, 31, and 13. Find the mean,
median and mode for this data set. Round any decimal answers to the nearest tenth. Did the
Raiders win all five games?
6. The mean score on a set of 15 exams is 74. What is the sum of the 15 exam scores?
7. A class of 12 students has taken an exam, and the mean of their scores is 71. One student takes the
exam late, and scores 92. After including the new score, what is the mean score for all 13 exams?
If you get a decimal answer, you should round to the nearest hundredth.
8. The twenty students in Mr. Edmondson’s class earned a mean score of 66 on an exam. Taking the
same exam, the ten students in Mrs. Wilkinson’s class earned a mean score of 86. What is the
mean when these teachers combine the scores of their students? If you get a decimal answer, you
should round to the nearest hundredth.
9. After 3 exams, Carl has a mean score of 78. With one exam remaining in the class, what is the
minimum score Carl will need on that exam to have an overall mean of 80?
10. Create a set of 6 data values in which the mean is higher than the median.
11. Can the mean be a negative number? Explain your answer and give an example.
12. The table at the right gives the ages of cars (in years) in a
supermarket parking lot. Using the information given in the
table, find the mean, median and mode of the data. Round any
decimal answers to the nearest tenth.
Age of the
Car
1
2
3
4
5
6
13. The following table gives the distance (in miles) students in a class
travel to get to campus. Using the information given in the table,
find the mean, median and mode of the data. Round any decimal
answers to the nearest tenth of a mile.
14. Given the list of courses and grades, calculate the GPA
of this student. For grade values, use the CSN values
listed earlier in this section. Round your answer to the
nearest hundredth.
15. Given the list of courses and grades, calculate the GPA of
this student. For grade values, use the CSN values listed
earlier in this section. Round your answer to the nearest
hundredth.
Course
Chemistry
Art
Spanish
Course
Math
English
History
P.E.
Number of
Cars
5
9
13
14
6
2
Miles
Traveled
2
5
8
12
15
20
30
Number of
Students
4
8
5
6
3
2
1
Credits
5
1
3
Grade
A
C
B
Credits
3
3
4
1
Grade
C+
B
C
A
16. Would it make sense to have a frequency table for a set of data without repeated values? Why or
why not?
Section 4.5 Exercises
1. Average class sizes at a college are given in the table on the right.
Create a bar graph that represents this data.
Class
Math
English
History
Philosophy
Size
34
27
22
17
2. The number of speeding tickets issued by the Mayberry police department during the months of
May, June and July of the years
1996, 1997, and 1998 are shown in
the graph on the right.
a. How many tickets were issued
in June of 1996?
b. For the months shown on the
graph, during which year was
the most tickets issued?
c. Over the three-year period, during which month was the most tickets issued?
3. A survey of college students, that asked them about the mode of transportation that they used to
travel to campus, resulted in the following information: 90 students drove a car to school, 70
students rode a bike, 60 students took the bus, and 20 students walked to school.
Find the number of degrees that should be given to each category, and create a pie chart that
represents this data.
4. In a Physics class, 4 students earned As, 9 earned Bs, 14 earned Cs, 7 got Ds, and 6 students got Fs.
Create a pie chart that represents this data.
5. A group of children purchased bags of jellybeans from a candy store. Later, they discovered five
of the bags contained 12 jellybeans, twelve bags contained 13 jellybeans, nine bags contained 14
jellybeans, and four bags had 15 beans. Use this data to create a relative frequency table and a bar
chart. Round all decimals to the nearest tenth.
6. The amount of time (in minutes) that it took a class of students to complete a short quiz was
recorded in the table below. Use the data to create a histogram.
Minutes
# of Students
4
3
5
5
6
4
7
1
8
2
9
8
10
12
7. Use the following data to create a Stem and Leaf plot:
15, 33, 31, 17, 13, 28, 26, 23, 35, 11, 17
8. Which type of graph would you use for the following set of data? Justify your choice.
Year
Population of Fictionland
1920
3,400
1940
3,900
1960
4,900
1980
6,300
2000
7,500
9. Which kind of graph is best for each of the following?
a. Displaying change over time.
b. Showing comparison and including the raw data.
c. Showing a comparison that displays the relative proportions.
10. If all the percent values for the sectors of a pie chart are added together, what is the total?
11. The pie chart shown below gives the percentage of 1990 US voters in each of six different age
groups. In 1990, there were 182,100,000 US citizens eligible to vote. How many people were in
each age group?