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Probability and Statistics
Final Exam Review
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
1) A single six-sided die is rolled. Find the probability of rolling a number less than 3.
1)
2) A study of 1000 randomly selected flights of a major airline showed that 782 of the flights
arrived on time. What is the probability of a flight arriving on time?
2)
3) If one card is drawn from a standard deck of 52 playing cards, what is the probability of
drawing an ace?
3)
4) In a survey of college students, 880 said that they have cheated on an exam and 1721 said
that they have not. If one college student is selected at random, find the probability that the
student has cheated on an exam.
4)
5) The distribution of blood types for 100 Americans is listed in the table. If one donor is
selected at random, find the probability of selecting a person with blood type A+ or A-.
5)
Blood Type O+
Number
37
O6
A+
34
A6
B+
10
B2
AB+
4
AB1
6) The distribution of Master's degrees conferred by a university is listed in the table.
6)
Major
Frequency
Mathematics
216
English
207
Engineering
75
Business
176
Education
222
What is the probability that a randomly selected student graduating with a Master's degree
has a major of Engineering? Round your answer to three decimal places.
7) Classify the statement as an example of classical probability, empirical probability, or
subjective probability. The probability that it will rain tomorrow is 24%.
7)
8) Classify the statement as an example of classical probability, empirical probability, or
subjective probability. The probability that a train will be in an accident on a specific route
is 1%.
8)
9) Classify the events as dependent or independent. Event A: A red candy is selected from a
package with 30 colored candies and eaten. Event B: A blue candy is selected from the
same package and eaten.
9)
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10) Classify the events as dependent or independent. The events of getting two aces when two
cards are drawn from a deck of playing cards and the first card is not replaced before the
second card is drawn.
10)
11) A group of students were asked if they carry a credit card. The responses are listed in the
table.
11)
Class
Freshman
Sophomore
Total
Credit Card Not a Credit Card
Carrier
Carrier
Total
46
14
60
32
8
40
78
22
100
If a student is selected at random, find the probability that he or she is a freshman given
that the student owns a credit card. Round your answers to three decimal places.
12) A group of students were asked if they carry a credit card. The responses are listed in the
table.
Class
Freshman
Sophomore
Total
12)
Credit Card Not a Credit Card
Carrier
Carrier
Total
14
46
60
17
23
40
31
69
100
If a student is selected at random, find the probability that he or she is a sophomore and
owns a credit card. Round your answers to three decimal places.
13) Find the probability of answering the two multiple choice questions correctly if random
guesses are made. Assume the questions each have five choices for the answer. Only one of
the choices is correct.
13)
14) A multiple-choice test has five questions, each with five choices for the answer. Only one
of the choices is correct. You randomly guess the answer to each question. What is the
probability that you answer the first two questions correctly?
14)
15) You are dealt two cards successively without replacement from a standard deck of 52
playing cards. Find the probability that the first card is a two and the second card is a ten.
Round your answer to three decimal places.
15)
16) Decide if the events A and B are mutually exclusive or not mutually exclusive, A die is
rolled.
A: The result is a 3.
B: The result is an odd number.
16)
17) Decide if the events A and B are mutually exclusive or not mutually exclusive. A card is
drawn from a standard deck of 52 playing cards.
A: The result is a club.
B: The result is a king.
17)
2
18) A card is drawn from a standard deck of 52 playing cards. Find the probability that the
card is an ace or a king.
18)
19) The events A and B are mutually exclusive. If P(A) = 0.2 and P(B) = 0.4, what is P(A or B)?
19)
20) Determine the probability distribution's missing value.
The probability that a tutor will see 0, 1, 2, 3, or 4 students
20)
x
0
1
2
3 4
P(x) 0.01 0.04 0.37 0.34 ?
21) State whether the variable is discrete or continuous.
The speed of a car on a Los Angeles freeway during rush hour traffic
21)
22) The random variable x represents the number of cars per household in a town of 1000
households. Find the probability of randomly selecting a household that has at least one
car.
22)
Cars Households
0
125
1
428
2
256
3
108
4
83
23) A sales firm receives an average of four calls per hour on its toll-free number. For any
given hour, find the probability that it will receive exactly nine calls. Use the Poisson
distribution.
23)
24) A company ships computer components in boxes that contain 30 items. Assume that the
probability of a defective computer component is 0.2. Use the geometric variance to find
the variance of defective parts.
24)
25) A car towing service company averages two calls per hour. Use the Poisson distribution to
determine the probability that in a randomly selected hour the number of calls is three.
25)
26) Assume that male and female births are equally likely and that the birth of any child does
not affect the probability of the gender of any other children. Find the probability of at
most three boys in ten births.
26)
27) State whether the variable is discrete or continuous.
The blood pressures of a group of students the day before their final exam
27)
28) The probability that an individual is left-handed is 0.11. In a class of 40 students, what is
the probability of finding five left-handers?
28)
29) A test consists of 10 multiple choice questions, each with five possible answers, one of
which is correct. To pass the test a student must get 60% or better on the test. If a student
randomly guesses, what is the probability that the student will pass the test?
29)
3
30) Basketball player Chauncey Billups of the Detroit Pistons makes free throw shots 88% of
the time. Find the probability that he misses his first shot and makes the second.
30)
31) A statistics professor finds that when he schedules an office hour at the 10:30 a.m. time slot,
an average of three students arrives. Use the Poisson distribution to find the probability
that in a randomly selected office hour no students will arrive.
31)
32) A test consists of 330 true or false questions. If the student guesses on each question, what
is the mean number of correct answers?
32)
33) Sixty-five percent of men consider themselves knowledgeable football fans. If 12 men are
randomly selected, find the probability that exactly two of them will consider themselves
knowledgeable fans.
33)
34) In a pizza takeout restaurant, the following probability distribution was obtained. The
random variable x represents the number of toppings for a large pizza. Find the mean and
standard deviation.
34)
x
0
1
2
3
4
P(x)
0.30
0.40
0.20
0.06
0.04
35) At a raffle, 10,000 tickets are sold at $5 each for three prizes valued at $4,800, $1,200, and
$400. What is the expected value of one ticket?
35)
36) State whether the variable is discrete or continuous.
The number of phone calls to the attendance office of a high school on any given school
day
36)
37) The probability that an individual is left-handed is 0.15. In a class of 70 students, what is
the mean and standard deviation of the number of left-handers in the class?
37)
38) In a raffle, 1,000 tickets are sold for $2 each. One ticket will be randomly selected and the
winner will receive a laptop computer valued at $1200. What is the expected value for a
person that buys one ticket?
38)
Decide which probability distribution -binomial, geometric, or Poisson- applies to the question. You do not need to
answer the question.
39) Given: The probability that a federal income tax return is filled out incorrectly with an
39)
error in favor of the taxpayer is 20%. Question: What is the probability that of the ten tax
returns randomly selected for an audit in a given week, three returns will contain only
errors favoring the taxpayer?
40) Given: The probability that a federal income tax return is filled out incorrectly with an
error in favor of the taxpayer is 20%. Question: What is the probability that of the ten tax
returns randomly selected for an audit, three returns will contain only errors favoring the
taxpayer?
4
40)
41) Given: The probability that a federal income tax return is filled out incorrectly with an
error in favor of the taxpayer is 20%. Question: What is the probability that when the ten
tax returns are randomly selected for an audit, the sixth return will contain only errors
favoring the taxpayer?
5
41)