This document serves as a review for statistics covering probability, discrete probability distributions, and counting principles. It includes definitions, sample problems, and detailed questions related to probabilities, combinations, permutations, and distributions, along with practical applications involving real-world scenarios. The content is structured with multiple-choice and open-ended questions designed to test understanding of statistical concepts.

1. 1
Statistics, Sample Test (Exam Review)
Module 2: Chapters 4 & 5 Review
Chapter 4 Probability
Chapter 5: Discrete Probability Distribution
Chapter 4 Probability
1. Definitions:
a. A simple event is _______________.
b. A sample space is ______________.
c. If two events are mutually exclusive, the probability that both will occur is _
d. The probability of an event is always ____________
e. The sum of probabilities of all final outcomes of an experiment is always _
2. Answer the following:
a. The number of Combinations of n items selected n at a time is ______
b. The number of Permutations of n items selected 0 at a time is ________
c. A pizza parlor offers 10 different toppings; how many four topping pizzas (different
toppings) are possible?
d. How many 6-letter code words can be made from the 26 letters of the alphabet if no
letter can be used more than once in the code word?
3. Answer the following:
a. A quiz consists of 3 true-false questions, how many possible answer keys are there?
Write out the sample space and tree diagram.
b. The sample space for tossing 5 coins consists of how many outcomes? Write out the
sample space.
4. A random sample of 100 people was asked if they were for or against the tax increase on rich
people. Of 60 males 45 were in favor, of all females 22 were in favor. Write the contingency
table and answer the following questions. (Hint: Make up a table like Table 4-1 of page 152.)
If one person is selected at random, find the probability that:
a) This person favors the tax increase on rich people.
b) This person is a female.
c) This person opposes the tax increase on rich people given that the person is a female.
d) This person is a male given that he favors the tax increase on rich people.
e) This person is a female and favors the tax increase on rich people.
f) This person opposes the tax increase on rich people or is a female.
g) Are the events “females” and opposes the tax increase on rich people independent?
Explain.
h) Are they mutually exclusive? Explain.

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5. Answer the following:
a. Find the probability of getting the outcome of “Tails and 2” when a coin is tossed and
a die is rolled.
b. A classic counting problem is to determine the number of different ways that the
letters of "PERSONNEL" can be arranged. Find that number.
6. A box consists of 14 red and 36 blue markers. If we select 3 different markers randomly,
a. What is the probability that they are all red? (With replacement)
b. What is the probability that they are all red? (Without a replacement) Draw a tree
diagram and label each branch.
7. If the probability of winning the race is 5/12,
a) What is the probability of losing the race?
b) What are odds against winning?
c) If the payoff odd is listed as 6:1, how much profit do you make if you bet $10 and
you win?
8. When two different people are randomly selected (from those in your class), find the
indicated probability (assume birthdays occur on the same day of the week with equal
frequencies).
a. Probability that two people are born on the same day of the week.
b. Probability that two people are both born on Monday.
9. How many different auto license plates are possible if the plate has?
a) 2 letters followed by 4 numbers?
b) 3 letters – no repeats, followed by 3 numbers - repetition allowed?
c) 4 letters – repetition allowed, followed by 2 numbers – no repeats?
d) 4 places – each character is either a letter or a number?
10. In a first-grade school class, there are ten girls and eight boys. In how many ways can:
a. the students finish first, second and third in a foot race? (Assume no ties)
b. the girls finish first and second in a geography contest? (Assume no ties)
c. three boys be selected for lunch duty?
d. six students be selected for a hockey team?
e. five students be selected: 3 boys and 2 girls?
f. four girls be selected for a field trip?

3. 3
Statistics, Sample Test (Exam Review)
Module 2: Chapters 4 & 5 Review
Chapter 5: Discrete Probability Distribution
1. Does the table describe probability distribution? What is the random variable, what are its
possiblevalues, and are its values numerical?
Number of Girls in 3 Births
Number of girls x P(x)
0 0.125
1 0.375
2 0.375
3 0.125
2. In a game, you pay 60 cents to select a 4-digit number. If you win by selecting the correct
4-digit number, you collect $3,000.
a) How many different selections are possible?
b) What is the probability of winning?
c) If you win, what is your net profit?
d) Write the Probability Distribution of Net Profit if you win.
e) Find the expected value and interpret.
3. A pharmaceutical company receives large shipments of aspirin tablets. The acceptance
sampling plan is to randomly select and test 24 tablets. The entire shipment is accepted if
at most 2 tablets do not meet the required specifications. If a particular shipment of
thousands of aspirin tablets actually has a 5.0% rate of defects, what is the probability
that this whole shipment will be accepted?
4. It is known that 70% of managers of all companies suffer from job related stress. What is
the probability that in a sample of 20 managers?
a) Exactly 8 suffer from job related stress.
b) At most 8 suffer from job related stress.
c) At least 9 suffer from job related stress.
d) Find the expected value.
e) Find the standard deviation.
f) Would it be unusual to claim that 7 managers from this sample suffer from job related
stress?
5. Find the probability of a couple having at least one girl among 3 children. (Discuss and
show all steps in two different methods.)
6. If an alarm clock has a 0.9 probability of working on any given morning.
a) What is the probability that it will not work?

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b) What is the probability that 2 such alarm clocks will not work?
c) What is the probability of being awakened if you have 2 such alarm clocks?
7. During an NFL Season there were 256 games played with 1307 touchdowns scored.
(Poisson distribution)
a. What was the mean number of touchdowns (TD) scored in each game during the
season? (Round the answer to the nearest 0.0001)
b. On Jan 10, 2010 the Green Bay Packers and Arizona Cardinals played a playoff
game in which there were 13 touchdowns scored. What is the probability that a
random game would have that many or more touchdowns?
c. Complete the chart at the right. The first column lists the number of
touchdowns in a game, this is filled in already. The second column is for the
predicted probability that a game chosen at random will have that many
touchdowns scored, calculate these values, round these values to the closest
0.0001. The third column is for your best prediction about the number of games
during the season that had that many touchdowns scored, round these values to
the closest whole number.
# Of TD Probability
(0.0001)
Whole Number: Predicted # of Games:
= 𝑷𝒓𝒐𝒃 𝑪𝒐𝒍𝒖𝒎𝒏 × 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒈𝒂𝒎𝒆𝒔 ( 𝒐𝒓 𝟐𝟓𝟔)
0
1
2
3
4
5
6
7
8
9