Unit 1 Homework
For all homework please place your answers on a separate sheet of paper. Make
sure that you show your work and when appropriate write your answers in
complete sentences. Read each question carefully. Reading and using language is
really important
1.1- Counting
1) A car company offers a series of options for their interiors in their new sports
car. An individual can have leather or cloth interior, a Bose sound system, a THX
sound system, or a stock sound system, and dark tinted windows or no tinting.
How many different kinds of cars can the company claim if each owner has a
choice of interior, sound system and windows? Draw a tree diagram to illustrate
your answer.
2) How many different words can you make using the following words:
a) Puzzle
b) Statistics
c) Antidisestablishmentarianism
3) Suppose that you are using two regular-sided dice. Answer the following
questions.
a) How many different values can you get from rolling the two dice?
b) How many different ways can you get a seven using the two dice?
c) How many different ways can you get less than five?
d) In the game of craps, rolling a two, three or twelve is called rolling craps.
How many ways can you roll craps on two fair dice?
e) The probability that you will roll craps is
The number of ways that you can roll craps
The total number of values that you can roll on the dice
Calculate the probability that you will roll craps on a single roll.
4) This one might take a little research. How many different California Lotto
MegaMillion tickets can you create? Make sure to explain your reasoning.
5) The probability of winning the lottery is:
The number of winning tickets
The total number of tickets
Calculate the probability that a ticket that you create will win the lottery. Given the
information that you have above, would you say that there is a good chance of
winning the lottery if you bought a single ticket? Use the probability and counting
to explain your reasoning.
6) Create a word problem of your own for each of the following kinds of techniques.
Then when you are finished writing the problem, answer it.
a) The Multiplicative Principle
b) Factorials
c) Combinations
d) Permutations
7) Discuss in your own words the difference between a combination and a
permutation. Detail how you could tell the difference between the two.
Unit 1.2a- Probability
For each question, make sure to show your work and when necessary write your
answers in complete sentences.
1) Suppose that you own a sandwich shop. For each sandwich, you can select one
meat, one cheese, and a one choice of bread. There are four kinds of meats, three
kinds of cheeses and two kinds of bread. Find the probability for each of the
situations.
a) The probability of selecting a sandwich that is made with roast beef.
b) The probability of selecting a sandwich with roast beef or ham.
c) The probability of selecting a sandwich with roast beef and cheddar.
d) The probability of selecting a sandwich with ham or cheddar.
e) The probability of selecting a sandwich made with roast beef or ham given
that the sandwich has cheddar cheese on it.
2) At a particular night club, 22% of the people in the club were African-American,
31% are Latino, 40% are Caucasian, and 7% are Asian-American. Answer the
following questions
a) Suppose that there are 600 people in the club. How many people are African
American? Caucasian? Asian-American? Latino?
b) Suppose that 60% of the Latino patron's are women? How many of the
patrons are Latino women?
c) Suppose that 55% of the African-American patron's are men. What is the
probability that you will select a patron at random that is an AfricanAmerican woman?
d) Suppose that 55% of the African American patron's are men and that 57% of
all of the patron's are women. What is the probability that you will select a
patron at random that is an African American or a woman?
3) The following numbers represent a randomly chosen group of 1000 Santa Ana
College students who are all taking transfer level mathematics. The following
are the demographics for these students. 45% of the students are taking Math
219 (6% are African-American, 52% are Latino, 32% are Asian, 10% are
Caucasian), 30% are taking Math 160 (10% are African American, 40% are
Latino, 35% are Asian-American, 15% are Caucasian) and 25% are taking Math
105 (4% are African American, 70% are Latino, 20% are Asian-American, and
6% are Caucasian). Construct a table with the ethnicity of the students as the
rows and the class that they took as the columns to help answer these questions.
The most informative way to set up the table is put the number of individuals
and not the percentage in each of the boxes in the table.
4)
5)
6)
7)
a) What percentage of the students in your survey are both Latino and taking
Math 219? What is the probability that you will select an individual who is
both Latino and taking Math 219?
b) What is the probability that you will select an individual at random that is a
Latino or an African American?
c) What is the probability that you will select an individual who is either a
Latino or a student in Math 219?
d) What is the probability that you will select an individual who is not Latino?
What is the probability that you select someone who is not Latino or is not
taking Math 160?
e) What is the probability that you will select an individual that is not AfricanAmerican given that the individual is taking Math 105?
Write and solve a probability problem using the tools that we have in Unit 1.2a.
For your problem construct a Venn Diagram that demonstrates the different sets
in your probability problem.
Give an example of an event that has a probability of zero.
Give an example of an event that has a probability of one.
Explain why it is impossible to have a probability of greater than 1.
Unit 1.2b
For each question, make sure to show your work and when necessary write your
answers in complete sentences.
1) Suppose that you conducted a study where you asked Santa Ana residents
whether or not they had been to Disneyland. You conducted a survey of 150
randomly chosen people. Of those 150 people, 95 of them said that they had
been to Disneyland.
a) What is the probability, if you selected without replacement, that the first
five people that you questioned would have gone to Disneyland? Explain
your reasoning.
b) Suppose that you put all of the responses in a hat and selected ones at
random with replacement, what is the probability that the first three that you
selected would not have gone to Disneyland? Explain your reasoning.
c) Suppose that you selected 20 responses at random, what is the probability
that all of the responses would have been from people who had been to
Disneyland? Explain your reasoning.
2) Suppose that you were given a jar filled with red, green and black beads. There
are 10 black beads, 25 red beads, and 17 green beads.
a) What is the probability, if you selected without replacement, that you would
select a black bead, then a red bead, then a green bead? What if you selected
the beads with replacement? Explain your reasoning.
b) Suppose that you wanted to figure out what the probability was that you
would select a green bead, a red bead, and a black bead from the jar without
replacement. What is the probability that you would do that?
c) What is the probability that you will select, with replacement, 5 consecutive
green beads? Would you say that this probability is likely? Explain your
reasoning.
d) Which is more likely, selecting 5 consecutive green beads with replacement
or 3 consecutive black beads with replacement?
3) Whenever we use statistics that are gathered from a large population, we
consider that any kind of probability we are doing with them is done with
replacement. Hence for each selection, the probabilities do not change (what is
the technical term for this?). Suppose that at Santa Ana College, 60% of the
students are Latino, 20% are Asian, 15% are Caucasian, 3% are African
American, and 2% are Native American.
a) If we walk into a classroom of 500 students that is roughly representative
(what do I mean by this term) of the population at Santa Ana College, how
many would we expect to be Latino? Asian? Caucasian? African American?
Native American? Explain your reasoning.
b) What is the probability that two students chosen at random will both be
Latino?
c) What is the probability that from 20 randomly selected students, none of
them will be Latino?
d) What is the probability that from 20 randomly selected students, at least one
of them will be Latino?
4) Conduct a short survey of 20 people chosen at random. Ask them which kind of
movie they prefer, comedy, action, horror, drama, cartoons. Then construct a
table like the one below. Then answer the questions.
Type of Movie
Number of people
responding
Percentage of the group
who chose the category
Comedy
Action
Horror
Drama
Cartoons
a) When you add up all of the probabilities, what is their sum? Explain how this
makes sense to you from a probability standpoint.
b) Suppose you chose two people at random from your sample. What is the
probability that You will select one who chose comedy and then one who
chose action, without replacement?
c) Would you say that your survey group accurately reflects the population of
all moviegoers in the United States? Why or why not? (Consider
demographic criteria such as age, race, socioeconomic status, level of
education, etc.)
d) What might be a better way to create your sample?
5) Which is more likely the probability of a series of events occurring if their
probability is calculated without replacement, or the probability of a series of
events occurring if their probability is calculated with replacement? Explain
your reasoning.
6) State whether or not the two events are independent or dependent. Explain
your reasoning.
a) Selecting a king from a deck of cards and then selecting a heart.
b) Rolling a six, a three, and then a 12 on a set of dice.
c) Selecting a Honda from a car lot and then selecting a Big Mac at MacDonald's
d) Selecting a woman from your gym and then selecting a woman from your
Stat's Class (assuming that no one in your Stat's class is actually a member of
your gym)
7) Write a multiplicative probability problem in which the events selected are
independent. Provide a solution to your problem as well.
8) Write a multiplicative probability problem in which the events selected are
dependent. Provide a solution to your problem as well.