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Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
PROBABILITY
Introduction
Provide an appropriate response.
1) Define mutually exclusive events and independent events. Give an example of each.
2) Give an example of events which are independent but not mutually exclusive.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
3)
Cause of Death
Cancer Heart Disease Other Total
Smoker
135
310
205
650
Nonsmoker
55
155
140
350
Total
190
465
345 1,000
Discuss the methods for finding the following two probabilities and explain the important differences in the
computations.
1) If one person is randomly selected, find the probability that he or she died of heart disease.
2) If one person is randomly selected, find the probability that he or she died of heart disease given that he or
she was a nonsmoker.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Answer Key
Testname: 12_1 PROBABILITIES_1 INTROD
1) Mutually exclusive events cannot occur simultaneously. Independent events are events for which one event does not
influence the outcome of the other. Examples will vary.
2) Answers will vary, but might include something like eating steak for supper and losing your car keys.
155
465
, using the total of 1,000 deaths, whereas probability 2 is , using only 350 nonsmokers in the
3) Probability 1 is 350
1,000
survey. The second probability is a conditional probability, referring only to the nonsmokers in the survey.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
PROBABILITY
Fundamentals
Express the indicated degree of likelihood as a probability value.
1) ʺYou have a 50-50 chance of choosing the correct answer.ʺ
1)
2) ʺThere is a 40% chance of rain tomorrow.ʺ
2)
Answer the question.
3) Which of the following cannot be a probability?
A) 1
B) -1
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
3)
1
C)
2
D) 0
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
4) On a multiple choice test with four possible answers for each question, what is the
probability of answering a question correctly if you make a random guess?
Find the indicated probability.
5) A sample space consists of 13 separate events that are equally likely. What is the
probability of each?
6) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on
the dice will be 5?
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
4)
5)
6)
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
7) A class consists of 46 women and 81 men. If a student is randomly selected, what is the
probability that the student is a woman?
7)
Answer the question, considering an event to be ʺunusualʺ if its probability is less than or equal to 0.05.
8) A multiple choice question has 16 possible answers, only one of which is correct. Is it
8)
ʺunusualʺ to answer a question correctly if a random guess is made?
9) Assume that a study of 500 randomly selected school bus routes showed that 486 arrived
on time. Is it ʺunusualʺ for a school bus to arrive late?
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
9)
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Estimate the probability of the event.
10) A polling firm, hired to estimate the likelihood of the passage of an up-coming
referendum, obtained the set of survey responses to make its estimate. The encoding
system for the data is: 0 = FOR, 1 = AGAINST. If the referendum were held today, estimate
the probability that it would pass.
10)
0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0
11) In a certain class of students, there are 9 boys from Wilmette, 5 girls from Kenilworth, 7
girls from Wilmette, 6 boys from Glencoe, 5 boys from Kenilworth and 3 girls from
Glenoce. If the teacher calls upon a student to answer a question, what is the probability
that the student will be from Kenilworth?
From the information provided, create the sample space of possible outcomes.
12) Flip a coin twice.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
11)
12)
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
13) Flip a coin three times.
Answer the question.
14) Find the odds against correctly guessing the answer to a multiple choice question with 4
possible answers.
15) In a certain town, 10% of people commute to work by bicycle. If a person is selected
randomly from the town, what are the odds against selecting someone who commutes by
bicycle?
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
13)
14)
15)
Answer Key
Testname: 12_2 PROBABILITIES_2 FUNDAMENTALS
1) 0.50
2) 0.40
3) B
1
4)
4
5)
1
13
6)
1
9
7)
46
127
8) No
9) Yes
10) 0.6
11) 0.286
12) HH HT TH TT
13) HHH HHT HTH HTT THH THT TTH TTT
14) 3 : 1
15) 9 : 1
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley