Deck 4: Probability

Question 1

Provide an appropriate response.
Discuss why the relative frequency method of computing probabilities might be chosen over the classical method.

Answer 1

Possible answers include the possibility that the experiment is so complicated that determining the
sample space for the classical is too difficult, or the ability to more quickly and easily conduct the
experiment by a simulation on a computer.

Question 2

Provide an appropriate response.
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?

Answer 2

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.

Question 3

Provide an appropriate response.

-If a game were "fair," the payoff on a bet would be the same as the odds for the event. In one game, the odds for winning are 1:13. If the game were "fair," what would the payoff be for a $5 bet? Of course, games in casinos are designed to make a profit for the casino investors. Supposing the casino makes the payoff at 1:11 odds, what profit does the casino make on your winning bet?

Answer 3

In a "fair" game the payoff would be $70 = 13·5 + 5 original bet. The casino payoff would be $60 = 11·5 + 5original bet. The profit would be $10.

Question 4

Provide an appropriate response.

-List two reasons it is better to sample without replacement when testing batches of products. When sampling without replacement, should you use the multiplication rule for independent or dependent events? Explain your answer.

Question 5

Provide an appropriate response.
Compare probabilities and odds. How can you convert odds to probabilities?

Question 6

Provide an appropriate response.
Under what circumstances can you sample without replacement and still use the multiplication rule for independence? Discuss population and sample size as you answer this question.

Question 7

Provide an appropriate response.
Probabilities are useful in the decision-making process. Suppose a random sample of 152 students was surveyed regarding an instructor's teaching. Suppose 105 students rated the instructor either excellent or above average on lecture presentations, 96 students rated the instructor as giving difficult or very difficult assignments and tests. Would you take this instructor for a class? Discuss the influence of probabilities on making this decision.

Question 8

Provide an appropriate response.
On an exam on probability concepts, Sue had an answer of for one problem. Explain how she knew that this result was incorrect.

Question 9

Provide an appropriate response.

-What important question must you answer before computing an "and" probability? How does the answer influence your computation?

Question 10

Provide an appropriate response.

-Discuss the differences, both in applications and in the formulas, for combinations and permutations. Give an example of each.

Question 11

Provide an appropriate response.
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?

Question 12

Provide an appropriate response.
Describe an event whose probability of occurring is 1 and explain what that probability means. Describe an event whose probability of occurring is 0 and explain what that probability means.

Question 13

Provide an appropriate response.
Discuss the advantages and disadvantages of odds.

Question 14

Provide an appropriate response.
Discuss the range of possible values for probabilities. Give examples to support each.

Question 15

Provide an appropriate response.

-Describe the process for making a tree diagram and give an example.

Question 16

Provide an appropriate response.

-Interpret the symbol P(B|A)and explain what is meant by the expression. What do we know if P(B|A)is not the same as P(B)?

Question 17

Provide an appropriate response.

-Define mutually exclusive events and independent events. Give an example of each.

Question 18

Provide an appropriate response.

-Give an example of events which are independent but not mutually exclusive.

Question 19

Provide an appropriate response.

-What important question must you answer before computing an "or" probability? How does the answer influence your computation?

Question 20

Provide an appropriate response.
When asked about the probability that he would become a sumo wrestler, Sam replied "slim to none." Relate that phrase to a numeric probability and interpret his meaning.

Question 21

Express the indicated degree of likelihood as a probability value.
"You have a 50-50 chance of choosing the correct answer."

A)0.9
B)0.25
C)50
D)0.50

Question 22

Express the indicated degree of likelihood as a probability value.

-"You cannot determine the exact decimal-number value of $\pi . "$

A)0
B)0.5
C)3.14
D)1

Question 23

Find the indicated probability

-If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap years.

A) $\frac { 1 } { 12 }$

B) $\frac { 1 } { 31 }$

C) $\frac { 1 } { 365 }$

D) $\frac { 31 } { 365 }$

Question 24

Answer the question.

-Which of the following cannot be a probability?

A) $\frac { 5 } { 3 }$

B) $\frac { 1 } { 2 }$

C) $\frac { 2 } { 3 }$

D) $\frac { 3 } { 5 }$

Question 25

Express the indicated degree of likelihood as a probability value.
"There is a 40% chance of rain tomorrow."

A)4
B)0.60
C)40
D)0.40

Question 26

Find the indicated probability

-A die with 12 sides is rolled. What is the probability of rolling a number less than 11?

A) 10
B) $\frac { 1 } { 12 }$

C) $\frac { 11 } { 12 }$

D) $\frac { 5 } { 6 }$

Question 27

Provide an appropriate response.
Suppose a student is taking a 5-response multiple choice exam; that is, the choices are A, B, C, D, and E, with only one of the responses correct. Describe the complement method for determining the probability of getting at least one of the questions correct on the 15-question exam. Why would the complement method be the method of choice for this problem?

Question 28

Find the indicated probability

-A sample space consists of 13 separate events that are equally likely. What is the probability of each?

A)1
B)0
C)13
D) $\frac { 1 } { 13 }$

Question 29

Answer the question.

-What is the probability of an event that is certain to occur?

A)0.95
B)1
C)0.5
D)0.99

Question 30

Express the indicated degree of likelihood as a probability value.
"Your mother could not have died two years before you were born."

A)0.25
B)0.5
C)1
D)0

Question 31

Find the indicated probability

-Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be 5?

A) $\frac { 8 } { 9 }$

B) $\frac { 1 } { 9 }$

C) $\frac { 5 } { 6 }$

D) 4

Question 32

Answer the question.

-What is the probability of an impossible event?

A)-1
B)1
C)0
D)0.1

Question 33

Answer the question.

-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) $\frac { 1 } { 2 }$

C) $\frac { 1 } { 4 }$

D) $\frac { 3 } { 4 }$

Question 34

Express the indicated degree of likelihood as a probability value.
"It will definitely turn dark tonight."

A)0.67
B)0.5
C)1
D)0.30

Question 35

Answer the question.

-Which of the following cannot be a probability?

A) $\frac { 1 } { 2 }$
B)-1
C)0
D)1

Question 36

Find the indicated probability

-On a multiple choice test, each question has 7 possible answers. If you make a random guess on the first question, what is the probability that you are correct?

A) 0
B) $\frac { 1 } { 7 }$
C) 7
D) 1

Question 37

Provide an appropriate response.

-Consider the following formulas: ${ } _ { n } P _ { r } = \frac { n ! } { ( n - r ) ! }$ and ${ } _ { n } C _ { r } = \frac { n ! } { ( n - r ) ! r ! }$
Given the same values for $\mathrm { n }$ and $\mathrm { r }$ in each formula, which is the smaller value, $\mathrm { P }$ or $\mathrm { C }$ ? How does this relate to th concept of counting the number of outcomes based on whether or not order is a criterion?

Question 38

Find the indicated probability

-A bag contains 2 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?

A) $\frac { 1 } { 5 }$

B) $\frac { 1 } { 7 }$

C) $\frac { 1 } { 3 }$

D) $\frac { 3 } { 10 }$

Question 39

Find the indicated probability

-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?

A) $\frac { 46 } { 81 }$

B) $\frac { 1 } { 127 }$

C) $\frac { 81 } { 127 }$

D) $\frac { 46 } { 127 }$

Question 40

Use the Poisson Distribution to find the indicated probability.
"You have one chance in ten of winning the race."

A)0.10
B)0.5
C)0.90
D)1

Question 41

Estimate the probability of the event.
In a certain class of students, there are 12 boys from Wilmette, 3 girls from Winnetka, 8 girls from Wilmette, 4 boys from Glencoe, 3 boys from Winnetka and 9 girls from Glenoce. If the teacher calls upon a student to answer a question, what is the probability that the student will be a boy?

A)0.308
B)0.487
C)0.767
D)0.41

Question 42

Find the indicated probability.
If a person told you in what month he was born, would it be "unusual" to guess the date of his birth (not including the year)?

A)Yes
B)No

Question 43

Estimate the probability of the event

-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?

A)0.25
B)0.37
C)0.286
D)0.143

Question 44

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05.
Assume that one student in your class of 31 students is randomly selected to win a prize. Would it be "unusual" for you to win?

A)No
B)Yes

Question 45

Estimate the probability of the event

-Of 1338 people who came into a blood bank to give blood, 253 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure.

A)0.157
B)0.189
C)0.24
D)0.108

Question 46

Friskie is having her fifth litter. The prior litters have either been three normal pups or two normal pups and a runt. Assume the probability of either outcome is 50%.

A)NNR NNN
B)N NN NR NNN NRN
C)NNN RNN NR
D)NR NNR NNR

Question 47

Both Fred and Ed have a bag of candy containing a lemon drop, a cherry drop, and a lollipop. Each takes out a piece and eats it. What are the possible pairs of candies eaten?

A) LD-LD CD-LD LP-LP LD-LP CD-CD LD-LP LP-CD CD-LD LP-LD
B) LD-LD CD-LD LP-LP LD-CD CD-CD LD-LP LP-CD CD-LP LP-LD
C) LD-CD LD-CD LD-CD LD-LP LD-LP LD-LP CD-LP CD-LP CD-LP
D) CD-LD LD-LP LP-CD LP-LP LD-LD

Question 48

From the information provided, create the sample space of possible outcomes

-Flip a coin twice.

A)HT TH
B)HH TT HT HT
C)HH HT TH TT
D)HH HT TT

Question 49

Find the indicated probability.
Is it "unusual" to get a 12 when a pair of dice is rolled?

A)No
B)Yes

Question 50

Find the indicated probability.
If you drew one card from a standard deck, would it be "unusual" to draw an ace of hearts?

A)Yes
B)No

Question 51

Find the indicated probability.
Assume that a study of 500 randomly selected school bus routes showed that 486 arrived on time. Is it "unusual" for a school bus to arrive late?

A)No
B)Yes

Question 52

Find the indicated probability.
If you are told that a mystery person's name begins with a consonant, would it be "unusual" to guess the first letter of that person's name?

A)Yes
B)No

Question 53

Find the indicated probability.
Is it "unusual" to get 9 when a pair of dice is rolled?

A)Yes
B)No

Question 54

Estimate the probability of the event

-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. 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0

A)0.65
B)0.6
C)0.4
D)0.5

Question 55

Find the indicated probability.
If you drew one card from a standard deck, would it be "unusual" to draw a 7?

A)Yes
B)No

Question 56

Find the indicated probability.
A multiple choice question has 16 possible answers, only one of which is correct. Is it "unusual" to answer a question correctly if a random guess is made?

A)No
B)Yes

Question 57

From the information provided, create the sample space of possible outcomes

-Flip a coin three times.

A) HH? ?TT ?TH TTT HTT THH H?T THT
B) H?? ??? ??? ??? ?H? THT TTH TTT
C) HH? TTT THT HTH HHT TTH HTH
D) HTT THT HTH HHH TTH TTT

Question 58

Find the indicated probability

-In a poll, respondents were asked whether they had ever been in a car accident. 196 respondents indicated that they had been in a car accident and 118 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident? Round to the nearest thousandth, if necessary.

A)0.376
B)0.624
C)0.005
D)1.661

Question 59

Estimate the probability of the event

-The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $90,000. Round your answers to the nearest tenth. $$\begin{array} { l } 104,000118,00084,000125,00087,000104,00090,00078,000139,000174,00081,00097,000132,00087,000118,000 \\111,00090,000146,00075,000111,000\end{array}$$

A)0.4
B)0.7
C)0.8
D)0.6

Question 60

Find the indicated probability.
Assume that a study of 300 randomly selected school bus routes showed that 272 arrived on time. Is it "unusual" for a school bus to arrive late?

A)Yes
B)No

Question 61

Determine whether the events are mutually exclusive

-Meet a man with an umbrella. Meet a man with a raincoat.

A)Yes
B)No

Question 62

Determine whether the events are mutually exclusive.

-A spinner has equal regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3?

A) $\frac { 2 } { 3 }$
B) 12
C) $\frac { 1 } { 3 }$
D) $\frac { 7 } { 9 }$

Question 63

Answer the question.
Suppose you are playing a game of chance. If you bet $7 on a certain event, you will collect $280 (including your $7 bet)if you win. Find the odds used for determining the payoff.

A)40 : 1
B)1 : 39
C)39 : 1
D)280 : 287

Question 64

From the information provided, create the sample space of possible outcomes

-Two white mice mate. The male has both a white and a black fur-color gene. The female has only white fur-color genes. The fur color of the offspring depends on the pairs of fur-color genes that they receive. Assume that neither the white nor the black gene dominates. List the possible outcomes. W = white and B = black

A)WW, BB
B)WB, BW
C)WW, WW
D)WW, BW

Question 65

Determine whether the events are mutually exclusive

-Draw one ball colored red from a bag. Draw one ball colored blue from the same bag.

A)No
B)Yes

Question 66

Answer the question

-Find the odds against correctly guessing the answer to a multiple choice question with 4 possible answers.

A)4 : 1
B)3 : 1
C)3 : 4
D)4 : 3

Question 67

Determine whether the events are mutually exclusive.
A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 5 wood and 10 graphite are defective and one racket is randomly selected from the sample, find the probability that the racket is wood or defective.

A)0.525
B)0.075
C)0.55
D)There is insufficient information to answer the question.

Question 68

Determine whether the events are mutually exclusive.

-Find $\mathrm { P } ( \overline { \mathrm { A } } )$ , given that $\mathrm { P } ( \mathrm { A } ) = 0.662$ .

A) 0
B) $1.511$
C) $1.662$
D) $0.338$

Question 69

Determine whether the events are mutually exclusive.

-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) $\frac { 1 } { 22 }$
B) $\frac { 9 } { 26 }$
C) $\frac { 11 } { 26 }$
D) $\frac { 25 } { 52 }$

Question 70

Determine whether the events are mutually exclusive

-Get a full time day job as a teller with a bank. Get a full time day job as a cashier at a store.

A)No
B)Yes

Question 71

Determine whether the events are mutually exclusive.
Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.206. Find the probability that in a given year it will not snow on January 1st in that town.

A)0.794
B)4.854
C)0.259
D)1.206

Question 72

Determine whether the events are mutually exclusive.

-If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.

A) $\frac { 334 } { 365 }$
B) $\frac { 31 } { 334 }$
C) $\frac { 11 } { 12 }$
D) $\frac { 31 } { 365 }$

Question 73

Determine whether the events are mutually exclusive

-Get stung by a bee. Get stung by a wasp.

A)No
B)Yes

Question 74

Answer the question

-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?

A)1 : 9
B)9 : 1
C)9 : 10
D)1 : 10

Question 75

Determine whether the events are mutually exclusive

-Find a ten dollar bill on the sidewalk. Find a ten dollar bill on the grass.

A)No
B)Yes

Question 76

Determine whether the events are mutually exclusive.
The probability that Luis will pass his statistics test is 0.42. Find the probability that he will fail his statistics test.

A)2.38
B)0.72
C)0.21
D)0.58

Question 77

Determine whether the events are mutually exclusive.

-The table below describes the smoking habits of a group of asthma sufferers. $$\begin{array} { r | c c c c c } & \text { Nonsmoker } & \begin{array} { c } \text { Occasional } \\\text { smoker }\end{array} & \begin{array} { c } \text { Regular } \\\text { smoker }\end{array} & \begin{array} { c } \text { Heavy } \\\text { smoker }\end{array} & \text { Total } \\\hline \text { Men } & 433 & 42 & 71 & 37 & 583 \\\text { Women } & 326 & 47 & 78 & 39 & 490 \\\text { Total } & 759 & 89 & 149 & 76 & 1073\end{array}$$ If one of the 1073 people is randomly selected, find the probability that the person is a man or a heavy smoker.

A)0.545
B)0.580
C)0.614
D)0.487

Question 78

Determine whether the events are mutually exclusive

-Go to a formal dinner affair. Wear blue jeans.

A)Yes
B)No

Question 79

Determine whether the events are mutually exclusive

-Read a book by Mark Twain. Read about Tom Sawyer.

A)No
B)Yes

Question 80

Determine whether the events are mutually exclusive.

-If $\mathrm { P } ( \mathrm { A } ) = \frac { 10 } { 11 }$ , find $\mathrm { P } ( \overline { \mathrm { A } } )$ .

A) $\frac { 1 } { 11 }$
B) 0
C) $\frac { 11 } { 10 }$
D) $\frac { 10 } { 21 }$