Download Chapter 4 - Practice Problems 1

Chapter 4 - Practice Problems 1
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
1) Compare the relative frequency formula for finding probabilities to the classical formula
for finding probabilities. How are the two formulas similar and how are they different?
What special requirements does the classical approach have?
2) Sometimes probabilities derived by the relative frequency method differ from the
probabilities expected from classical probability methods. How does the law of large
numbers apply in this situation?
3) On an exam on probability concepts, Sue had an answer of 13
for one problem. Explain
8
1)
2)
3)
how she knew that this result was incorrect.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Express the indicated degree of likelihood as a probability value.
4) ʺThere is a 40% chance of rain tomorrow.ʺ
A) 40
B) 0.60
4)
C) 0.40
D) 4
5) ʺYou have one chance in ten of winning the race.ʺ
A) 0.10
5)
B) 0.5
C) 0.90
D) 1
Answer the question.
6) 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?
A) 1
B)
1
4
C)
1
3
4
D)
1
2
6)
Find the indicated probability.
7) A sample space consists of 176 separate events that are equally likely. What is the probability of
each?
1
A) 176
B) 0
C) 1
D)
176
Answer the question, considering an event to be ʺunusualʺ if its probability is less than or equal to 0.05.
8) Is it ʺunusualʺ to get a sum of 12 when a pair of dice is rolled?
A) Yes
7)
8)
B) No
9) Assume that a study of 300 randomly selected school bus routes showed that 276 arrived on time.
Is it ʺunusualʺ for a school bus to arrive late?
A) No
9)
B) Yes
From the information provided, create the sample space of possible outcomes.
10) Flip a coin three times.
10)
A) HTT THT HTH HHH TTH TTT
B) HHH HHT HTH HTT THH THT TTH TTT
C) HHH HTT HTH TTT HTT THH HHT THT
D) HHH TTT THT HTH HHT TTH HTH
Determine whether the events are disjoint.
11) Draw one ball colored red from a bag.
Draw one ball colored blue from the same bag.
11)
A) No
B) Yes
12) Find a ten dollar bill on the sidewalk.
Find a ten dollar bill on the grass.
12)
A) No
B) Yes
Estimate the probability of the event.
13) 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:
1 = FOR, 2 = AGAINST. If the referendum were held today, estimate the probability that it would
pass.
13)
1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1
A) 0.6
B) 0.5
C) 0.65
D) 0.4
Find the indicated probability.
3
14) If P(A) = , find P(A).
16
A)
3
19
14)
B)
16
3
C)
2
13
16
D) 0
15) If you pick a card at random from a well shuffled deck, what is the probability that you get a face
card or a spade?
A)
1
22
B)
9
26
C)
11
26
D)
15)
25
52
16) The manager of a bank recorded the amount of time each customer spent waiting in line during
peak business hours one Monday. The frequency table below summarizes the results.
16)
Waiting Time Number of
(minutes) Customers
14
0-3
9
4-7
15
8-11
6
12-15
8
16-19
2
20-23
1
24-27
If we randomly select one of the customers represented in the table, what is the probability that the
waiting time is at least 12 minutes or between 8 and 15 minutes?
A) 0.109
B) 0.582
C) 0.691
D) 0.677
17) A 6-sided die is rolled. Find P(3 or 5).
A) 2
B)
17)
1
36
C)
1
6
D)
1
3
18) 100 employees of a company are asked how they get to work and whether they work full time or
part time. The figure below shows the results. If one of the 100 employees is randomly selected,
find the probability that the person drives alone or cycles to work.
1. Public transportation: 6 full time, 8 part time
2. Bicycle: 4 full time, 4 part time
3. Drive alone: 30 full time, 34 part time
4. Carpool: 7 full time, 7 part time
A) 0.64
B) 0.68
C) 0.72
3
D) 0.34
18)
Is Event B dependent or independent of Event A?
19) A: A green ball is drawn from a box with five balls and placed next to the box.
B: A red ball is drawn next and placed next to the green one.
A) Independent
19)
B) Dependent
Find the indicated probability.
20) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore
leap years.
A)
11
12
B)
31
334
C)
31
365
D)
334
365
21) A die with 8 sides is rolled. What is the probability of rolling a number less than 7?
A)
3
4
B) 6
C)
7
8
D)
21)
1
8
22) If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap
years.
A)
31
365
B)
1
365
C)
1
31
D)
50
81
B)
1
81
C)
31
81
D)
B) 0.360
C) 0.720
5
6
B)
6
5
C)
4
1
7776
24)
D) 0.130
25) Find the probability of correctly answering the first 5 questions on a multiple choice test if random
guesses are made and each question has 6 possible answers.
A)
23)
50
31
24) In one town, 36% of all voters are Democrats. If two voters are randomly selected for a survey, find
the probability that they are both Democrats.
A) 0.126
22)
1
12
23) A class consists of 50 women and 31 men. If a student is randomly selected, what is the probability
that the student is a woman?
A)
20)
D)
1
15625
25)
Answer Key
Testname: CH 4 SET 1
1) In the relative frequency formula, the probabilities are determined by conducting an experiment, counting the number
of occurrences of the event, and creating the ratio of number of occurrences to number of times the experiment was
conducted. In the classical approach, a sample space of all of the possible simple events is created and the number of
successes is compared to the number of different simple events. In the classical approach, each outcome must be
equally likely.
2) The law of large numbers states that as an experiment is repeated again and again, the relative frequency probabilities
tend to approach the actual probabilities expected from the classical approach.
3) Probabilities cannot exceed 1.
4) C
5) A
6) B
7) D
8) A
9) A
10) B
11) B
12) A
13) A
14) C
15) C
16) B
17) D
18) C
19) B
20) D
21) A
22) A
23) A
24) D
25) C
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