Deck 13: From Randomness to Probability

Question 1

What is the probability of an event?

A)A number between 0 and 1 that reports the likelihood of the event's occurrence
B)A collection of outcomes
C)A single attempt or realization of a random phenomenon
D)Its long-run relative frequency
E)Two of the above

Answer 1

Two of the above

Question 2

A random spinner can land on red,green,blue,or yellow.If on the first three spins it lands once each on red,green,and yellow,is it more likely to land on blue on the fourth spin?

A)Yes,because every color is equally likely to occur.
B)Yes,because the Probability Assignment Rule dictates that all outcomes should occur.
C)No,because the spins are disjoint events.
D)Yes,because the spinner shows randomness,not chaos.
E)No,because knowing one outcome will not affect the next.

Answer 2

No,because knowing one outcome will not affect the next.

Question 3

Toss a coin five times;record the number of heads.

A){0,1,2,3,4,5},equally likely
B){0,1,2,3,4,5},not equally likely
C){1,2,3,4,5},equally likely
D){1,2,3,4,5},not equally likely
E){1,2},equally likely

Answer 3

{0,1,2,3,4,5},not equally likely

Question 4

The Addition Rule says that P(A or B)= P(A)+ P(B).What must be true about events A and B for this rule to apply?

A)The events must be disjoint.
B)The events must be independent.
C)The events must be mutually exclusive.
D)Two of the above

Question 5

At the horse racing track,a gambler bets on the wrong horse in a 10-horse field nine times in a row.Later,when talking to a friend,he said he was confident that he would pick the winner the next time,because he was "due to pick a winner." Comment on his reasoning.

A)This is false reasoning because he doesn't appear to be lucky.
B)This is false reasoning because there is no Law of Averages for independent events.
C)When there are 10 horses in a race and he has chosen the wrong horse nine times in a row,he statistically should pick a winner the next time.
D)If he doesn't pick the winning horse the next time,he will shortly after that.
E)None of the above apply.

Question 6

Roll a die eight times;record the length of the longest run of sixes.

A){0,1,2,3,4,5,6,7,8},not equally likely
B){0,1,2,3,4,5,6,7,8},equally likely
C){0,1,2,3,4,5,6},not equally likely
D){1,2,3,4,5,6,7,8},not equally likely
E){1,2,3,4,5,6},equally likely

Question 7

Roll an ordinary die;record the number.

A){1,2,3,4,5,6},not equally likely
B){1,6},equally likely
C){1,2,3,4},equally likely
D){1,6},not equally likely
E){1,2,3,4,5,6},equally likely

Question 8

Roll two dice;record the positive difference.

A){0,6},not equally likely
B){0,1,2,3,4,5},not equally likely
C){1,2,3,4,5,6},equally likely
D){0,1,2,3,4,5},equally likely
E){1,2,3,4,5,6},not equally likely

Question 9

Which of the following are equivalent to the probability of the complement of event A?
(i)P(
)
(ii)1 - P(A does not occur)
(iii)1 - P(A occurs)
(iv)P(A does not occur)

A)ii
B)i,iii,and iv
C)i and iii
D)i,ii,and iv
E)iii and iv

Question 10

When a weather forecaster predicts a 20% chance of thunderstorms,is this an empirical probability,theoretical probability,or personal probability?

A)Theoretical probability.
B)Empirical probability.
C)Personal probability.
D)None of the above.
E)All of the above.

Question 11

The weather reporter predicts that there is a 20% chance of snow tomorrow for a certain region.What is meant by this phrase?

A)Snow occurs 20% of the time in this region.
B)The occurrence of snow is "truly random" and will occur 20% of the time.
C)In circumstances "like this," snow occurs 20% of the time.
D)20% of the time it snows on this date.
E)It will rain 20% of the day tomorrow.

Question 12

Roll two dice;record the smaller number.

A){1,2,3,4,5,6},not equally likely
B){1,2,3,4,5},equally likely
C){0,1,2,3,4,5},equally likely
D){1,2,3,4,5,6},equally likely
E){1,2,3,4,5},not equally likely

Question 13

Toss a coin three times;record the order of heads and tails.

A){HHH,HHT,TTH,TTT},equally likely
B){HHH,HHT,HTH,HHT,HTT,THT,TTH,TTT},equally likely
C){HHH,HHT,TTH,TTT},not equally likely
D){H,T},equally likely
E){HHH,HHT,HTH,HHT,HTT,THT,TTH,TTT},not equally likely

Question 14

Pick 5 cards from a standard deck without replacement;record the number of eights.

A){0,1,2,3,4},not equally likely
B){1,2,3,4,5,6,7,8},equally likely
C){0,1,2,3,4,5},not equally likely
D){1,2,3,4},not equally likely
E){0,1,2,3,4,5,6,7,8},equally likely

Question 15

Roll a die and record the number.Then flip a coin and record whether it comes up heads or tails.

A){1H,1T,2H,2T,3H,3T,4H,4T,5H,5T,6H,6T},equally likely
B){1H,1T,2H,2T,3H,3T,4H,4T,5H,5T,6H,6T},not equally likely
C){1,2,3,4,5,6,H,T},not equally likely
D){1H,1T,2H,2T,3H,3T,4H,4T,5H,5T,6H,6T,HH,HT,TH,TT},equally likely
E){1H,2T,3H,4T,5H,6T},equally likely

Question 16

The sum of the probabilities of all possible outcomes of a trial must be 1.What rule or law is this?

A)The Law of Large Numbers
B)The Probability Assignment Rule
C)The Total Probability Rule
D)The Rule of Law
E)The Law of Averages

Question 17

The Multiplication Rule says that P(A and B)= P(A)× P(B).What must be true about events A and B for this rule to apply?

A)The events must be disjoint.
B)The events must be independent.
C)The events must be mutually exclusive.
D)Two of the above

Question 18

A family has two children;record the genders in order of birth.

A){BB,BG,GG},equally likely
B){BB,BG,GB,GG},equally likely
C){BB,BG,GG},not equally likely
D){BB,BG,GB,GG},not equally likely
E){B,G},equally likely

Question 19

Pick cards from a deck until you get a black card or 4 consecutive red cards;record the cards in order.

A){BBBB,RBBB,RRBB,RRRB,RRRR},not equally likely
B){B,RB,RRB,RRRB,RRRRB,RRRRRB,....},not equally likely
C){B,RB,RRB,RRRB,RRRRB},not equally likely
D){B,RB,RRB,RRRB,RRRR},not equally likely
E){BBBB,BBBR,BBRB,BBRR,BRBB,BRBR,BRRB,BRRR,RBBB,RBBR,RBRB,RBRR,RRBB,RRBR,RRRB,RRRR},equally likely

Question 20

A telemarketer is almost through with her entire shift,and she has not made a single sale.Her manager says that she has a good chance of making a sale on her last few phone calls because she is due.Is her manager right?

A)No,because the Probability Assignment Rule applies in the long-run,not in the short-run.
B)Yes,because the Law of Averages is valid for independent events.
C)No,because there is no Law of Large Numbers for independent events.
D)Yes,because the Law of Large Numbers is valid for independent events.
E)No,because there is no Law of Averages for independent events.

Question 21

The plastic arrow on a spinner for a child's game stops rotating to point at one of four colours that will determine what happens next.Determine whether the following probability assignment is legitimate.
Probability of ...

A)Legitimate
B)Not legitimate

Question 22

Many stores run "secret sales": Shoppers receive cards that determine how large a discount they get,but the percentage is revealed by scratching off that black stuff only after the purchase has been totaled at the cash register.The store is required to reveal (in the fine print)the distribution of discounts available.Determine whether the following probability assignment is legitimate.
Probability of ...

A)Legitimate
B)Not legitimate

Question 23

Many stores run "secret sales": Shoppers receive cards that determine how large a discount they get,but the percentage is revealed by scratching off that black stuff only after the purchase has been totaled at the cash register.The store is required to reveal (in the fine print)the distribution of discounts available.Determine whether the following probability assignment is legitimate.
Probability of ...

A)Legitimate
B)Not legitimate

Question 24

In a business class,33% of the students have never taken a statistics class,42% have taken only one semester of statistics,and the rest have taken two or more semesters of statistics.The professor randomly assigns students to groups of three to work on a project for the course.What is the probability that the first group mate you meet has studied no more than one semester of statistics?

A)0.42
B)0.25
C)0.58
D)0.75
E)0.33

Question 25

According to a survey conducted by an environmental organization,the probability that an eligible voter cares about environmental issues is 0.61,the probability that an eligible voter voted in the last election is 0.44 and the probability that an eligible voter both voted in the last election and cares about environmental issues is 0.30.Are caring about environmental issues and voting in the last election disjoint events?

A)Yes,the probability that a voter cares about environmental issues is the same as the probability that a voter cares about environmental issues given that they voted in the last election.
B)No,30% both care about environmental issues and voted in the last election
C)No,the probability that a voter voted in the last election is 0.44,but the probability that a voter voted in the last election given that they care about environmental issues is 0.49.
D)Yes,the probability that a voter cares about environmental issues and voted in the last election is zero.
E)Yes,because P(C or V)= P(C)+ P(V)

Question 26

A consumer organization estimates that 34% of the households in a particular community have one television set,39% have two sets,and 20% have three or more sets.What is the probability that a household chosen at random has no more than one television set?

A)0.41
B)0.59
C)0.07
D)0.34
E)0.46

Question 27

The plastic arrow on a spinner for a child's game stops rotating to point at one of four colours that will determine what happens next.Determine whether the following probability assignment is legitimate.
Probability of ...

A)Legitimate
B)Not legitimate

Question 28

A consumer organization estimates that 35% of the households in a particular community have one television set,36% have two sets,and 24% have three or more sets.What is the probability that a household chosen at random has no television sets?

A)0.05
B)0.09
C)0
D)0.95
E)0.11

Question 29

Many stores run "secret sales": Shoppers receive cards that determine how large a discount they get,but the percentage is revealed by scratching off that black stuff only after the purchase has been totaled at the cash register.The store is required to reveal (in the fine print)the distribution of discounts available.Determine whether the following probability assignment is legitimate.
Probability of ...

A)Legitimate
B)Not legitimate

Question 30

An online poll asked people what their main source of news was: newspapers,television,internet,or radio? There were 866 responses.Here are the results:
If we select a person at random from this sample of 912 people,what is the probability that the person responded "Internet" or "Radio"?

A)0.114
B)0.669
C)0.331
D)0.217
E)302

Question 31

An online poll asked people what their main source of news was: newspapers,television,internet,or radio? There were 882 responses.Here are the results:
If we select a person at random from this sample of 917 people,what is the probability that the person responded "Newspapers"?

A)0.130
B)0.242
C)0.177
D)0.430
E)0.264

Question 32

The plastic arrow on a spinner for a child's game stops rotating to point at one of four colours that will determine what happens next.Determine whether the following probability assignment is legitimate.
Probability of ...

A)Legitimate
B)Not legitimate

Question 33

In a survey of women who were asked to name their favorite colour,16% said blue,19% said red,19% said green,12% said yellow,and 11% said black.If you pick a survey participant at random,what is the probability that she named a colour different from the aforementioned colours?

A)0.16
B)0.23
C)0.77
D)0.20
E)0.82

Question 34

In a business class,25% of the students have never taken a statistics class,35% have taken only one semester of statistics,and the rest have taken two or more semesters of statistics.The professor randomly assigns students to groups of three to work on a project for the course.What is the probability that the first group mate you meet has studied some statistics?

A)0.65
B)0.60
C)0.35
D)0.40
E)0.75

Question 35

The plastic arrow on a spinner for a child's game stops rotating to point at one of four colours that will determine what happens next.Determine whether the following probability assignment is legitimate.
Probability of ...

A)Legitimate
B)Not legitimate

Question 36

In a business class,40% of the students have never taken a statistics class,15% have taken only one semester of statistics,and the rest have taken two or more semesters of statistics.The professor randomly assigns students to groups of three to work on a project for the course.What is the probability that the first group mate you meet has studied two or more semesters of statistics?

A)0.55
B)0.85
C)0.15
D)0.45
E)0.60

Question 37

The plastic arrow on a spinner for a child's game stops rotating to point at one of four colours that will determine what happens next.Determine whether the following probability assignment is legitimate.
Probability of ...

A)Legitimate
B)Not legitimate

Question 38

Many stores run "secret sales": Shoppers receive cards that determine how large a discount they get,but the percentage is revealed by scratching off that black stuff only after the purchase has been totaled at the cash register.The store is required to reveal (in the fine print)the distribution of discounts available.Determine whether the following probability assignment is legitimate.
Probability of ...

A)Legitimate
B)Not legitimate

Question 39

In a survey of women who were asked to name their favorite colour,18% said blue,16% said red,17% said green,12% said yellow,and 14% said black.If you pick a survey participant at random,what is the probability that her favorite colour is yellow or black?

A)0.14
B)0.26
C)0.74
D)0.12
E)0.34

Question 40

Many stores run "secret sales": Shoppers receive cards that determine how large a discount they get,but the percentage is revealed by scratching off that black stuff only after the purchase has been totaled at the cash register.The store is required to reveal (in the fine print)the distribution of discounts available.Determine whether the following probability assignment is legitimate.
Probability of ...

A)Legitimate
B)Not legitimate

Question 41

The contingency table below provides a joint frequency distribution for a random sample of patients at a hospital classified by blood type and sex.
If a person is selected at random from the sample,find the probability that the person has blood type A and is female.

A)0.746
B)0.590
C)0.244
D)0.990
E)0.422

Question 42

In a survey of women who were asked to name their favorite colour,17% said blue,18% said red,18% said green,14% said yellow,and 11% said black.If you pick a survey participant at random,what is the probability that her favorite colour is not red?

A)0.72
B)0.82
C)0.18
D)0.8
E)0.60

Question 43

The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement.
Suppose one of these people is selected at random.Compute the probability that the person selected was a store clerk.

A)0.084
B)0.099
C)0.316
D)0.267
E)0.026

Question 44

A survey of the male students at a junior college reveals that,26% play soccer regularly,22% are Latino,and half of the Latino students play soccer regularly.If a male student is selected at random,what is the probability that he is neither Latino nor a soccer player?

A)0.89
B)0.52
C)0.63
D)0.26
E)0.41

Question 45

Melissa is looking for the perfect man.She claims that of the men at her college,36% are smart,26% are funny,and 13% are both smart and funny.If Melissa is right,what is the probability that a man chosen at random from her college is neither funny nor smart?

A)0
B)0.87
C)0.64
D)0.51
E)0.38

Question 46

The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement.
Find the probability that the person was an attorney and retired before the age of 61.

A)0.190
B)0.267
C)0.048
D)0.062
E)0.499

Question 47

The probability that a student at a certain college is male is 0.47.The probability that a student at that college has a job off campus is 0.22.The probability that a student at the college is male and has a job off campus is 0.12.If a student is chosen at random from the college,what is the probability that the student is male or has an off campus job?

A)0.57
B)0
C)0.81
D)0.69
E)0.45

Question 48

Of the coffee makers sold in an appliance store,6.0% have either a faulty switch or a defective cord,2.4% have a faulty switch,and 0.3% have both defects.What percent of the coffee makers will have a defective cord?

A)97.6%
B)6.0%
C)3.9%
D)6.3%
E)2.7%

Question 49

A survey revealed that 50% of people are entertained by reading books,34% are entertained by watching TV,and 16% are entertained by both books and TV.What is the probability that a person will be entertained by either books or TV?

A)1
B)0.32
C)0.84
D)0.16
E)0.68

Question 50

The contingency table below provides a joint frequency distribution for a random sample of patients at a hospital classified by blood type and sex.
If a person is selected at random from the sample,find the probability that the person has blood type B.

A)0.577
B)0.080
C)0.090
D)0.514
E)0.046

Question 51

At a California college,17% of students speak Spanish,6% speak French,and 2% speak both languages.What is the probability that a student chosen at random from the college speaks Spanish but not French?

A)0.11
B)0.13
C)0.21
D)0.15
E)0.04

Question 52

The table below describes the smoking habits of a group of asthma sufferers.
If one of the 1,034 subjects is randomly selected,find the probability that the person chosen is a female nonsmoker.

A)0.380
B)0.540
C)0.551
D)0.849
E)0.704

Question 53

The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement.
Find the probability that the person was a secretary or retired before the age of 61.

A)0.465
B)0.286
C)0.090
D)0.555
E)0.414

Question 54

The contingency table below provides a joint frequency distribution for a random sample of patients at a hospital classified by blood type and sex.
If a person is selected at random from the sample,find the probability that the person has blood type A or is female.

A)0.985
B)0.767
C)0.378
D)0.535
E)0.218

Question 55

An auto insurance company was interested in investigating accident rates for drivers in different age groups.The following contingency table was based on a random sample of drivers and classifies drivers by age group and number of accidents in the past three years.
If one of these drivers is selected at random,find the probability that the person has had no accidents in the last three years or is younger than 25.

A)0.935
B)0.138
C)0.594
D)0.196
E)0.797

Question 56

The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement.
Suppose one of these people is selected at random.Compute the probability that the person selected was an attorney who retired between 61 and 65.

A)0.401
B)0.106
C)0.264
D)0.249
E)0.424

Question 57

Employment data at a software company reveal that 41% of employees have a computer science degree,36% are women and half of the women have a computer science degree.What is the probability that a randomly chosen employee is female or has a computer science degree?

A)0.77
B)0.23
C)0.18
D)0.41
E)0.59

Question 58

A survey of senior citizens at a doctor's office shows that 45% take blood pressure-lowering medication,41% take cholesterol-lowering medication,and 14% take both medications.What is the probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication?

A)0.18
B)0.72
C)0
D)1
E)0.86

Question 59

According to a survey conducted by an environmental organization,the probability that an eligible voter cares strongly about environmental issues is 0.57,the probability that an eligible voter votes regularly is 0.46 and the probability that an eligible voter both votes regularly and care strongly about environmental issues is 0.28.If an eligible voter is selected at random what is the probability that the person cares strongly about environmental issues but does not vote regularly?

A)0.11
B)0.01
C)0.57
D)0.29
E)0.72

Question 60

According to a survey in one U.S.city,49% of women between the ages and 25 of 35 are married,47% are working full time,and 21% are married and working full time.If a woman between the ages of 25 and 35 is picked at random from the city,what is the probability that she is working full time or married but not both?

A)0.79
B)0.25
C)0.75
D)0.54
E)0.96

Question 61

An auto insurance company was interested in investigating accident rates for drivers in different age groups.The following table was based on a random sample of drivers and classifies drivers by age group and accident rate.
Suppose one of these people is selected at random.Compute the probability that the person is aged over 45 and has had no accidents in the past three years.

A)0.382
B)0.089
C)0.484
D)0.537
E)0.789

Question 62

The table shows the political affiliation of voters in one city and their positions on raising taxes.
What is the probability that a randomly picked person votes Conservative and opposes raising taxes?

A)0.321
B)0.400
C)0.530
D)0.425
E)0.170

Question 63

An auto insurance company was interested in investigating accident rates for drivers in different age groups.The following table was based on a random sample of drivers and classifies drivers by age group and accident rate.
Suppose one of these people is selected at random.Compute the probability that the person has had more than one accident in the past three years.

A)0.232
B)0.240
C)0.061
D)0.025
E)0.301

Question 64

An auto insurance company was interested in investigating accident rates for drivers in different age groups.The following table was based on a random sample of drivers and classifies drivers by age group and accident rate.
Suppose one of these people is selected at random.Compute the probability that the person is aged over 45.

A)0.539
B)0.375
C)0.094
D)0.776
E)0.484