Deck 14: Probability Rules

Question 1

According to a survey conducted by an environmental organization,the probability that an eligible voter cares strongly about environmental issues is 0.60,the probability that an eligible voter votes regularly is 0.48 and the probability that an eligible voter both votes regularly and care strongly about environmental issues is 0.270.What is the probability that someone who cares strongly about environmental issues votes regularly?

A)0.270
B)0.810
C)0.450
D)0.563
E)0.210

Answer 1

0.450

Question 2

In a language program at a university,14% of students speak Spanish,7% speak French,and 4% speak both languages.A student is chosen at random from the college What is the probability that a student who speaks Spanish also speaks French?

A)0.170
B)0.286
C)0.030
D)0.040
E)0.571

Answer 2

0.286

Question 3

The table shows the political affiliation of voters in one city and their positions on raising taxes.
Raising Taxes
What is the probability that a voter who favours raising taxes is an NDP supporter?

A)0.120
B)0.520
C)0.400
D)0.231
E)0.300

Answer 3

0.231

Question 4

You draw a card at random from a standard deck of 52 cards.Find the probability that the card is a face card given that it is a king.

A)0.077
B)0.333
C)0.231
D)1
E)0.25

Question 5

The table shows the political affiliation of voters in one city and their positions on raising taxes.
Raising Taxes
What is the probability that a Conservative supporter opposes raising taxes?

A)0.560
B)0.360
C)0.232
D)0.361
E)0.130

Question 6

You draw a card at random from a standard deck of 52 cards.Find the probability that the card is a three given that it is not a face card.

A)0.1
B)0.25
C)1
D)0.769
E)0.077

Question 7

A group of volunteers for a clinical trial consists of 79 women and 77 men.20 of the women and 18 of the men have high blood pressure.If one of the volunteers is selected at random find the probability that the person is a man given that they have high blood pressure.

A)0.494
B)0.474
C)0.234
D)0.244
E)0.115

Question 8

If a single fair die is rolled,find the probability of a 5 given that the number rolled is odd.

A)

B)

C)

D)

E)1

Question 9

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.
What is the probability that a person who had no accidents in the past three years is over 45?

A)0.364
B)0.752
C)0.484
D)0.522
E)0.697

Question 10

The table below describes the smoking habits of a group of asthma sufferers.
What is the probability that a woman is a nonsmoker?

A)0.307
B)0.689
C)0.468
D)0.656
E)0.445

Question 11

The table below describes the smoking habits of a group of asthma sufferers.
What is the probability that a light smoker is a woman?

A)0.680
B)0.164
C)0.550
D)0.085
E)0.156

Question 12

A group of volunteers for a clinical trial consists of 81 women and 83 men.19 of the women and 21 of the men have high blood pressure.If one of the volunteers is selected at random find the probability that the person has high blood pressure given that it is a woman.

A)0.244
B)0.475
C)0.116
D)0.494
E)0.235

Question 13

University students were given three choices of pizza toppings and asked to choose one favorite.They were also asked what year of their program they were in.The following table shows the results.
If a student responded "meat",what is the probability that they are in the third year of their program?

A)0.064
B)0.194
C)0.13
D)0.310
E)0.224

Question 14

You draw a card at random from a standard deck of 52 cards.Find the probability that the card is a heart given that it is black.

A)0.077
B)0
C)0.333
D)0.25
E)0.5

Question 15

The table shows the careers of a group of retired people and their ages at retirement.
What is the probably that a person who was an attorney retired between the ages of 50 and 55?

A)0.012
B)0.264
C)0.080
D)0.045
E)0.150

Question 16

The table shows the careers of a group of retired people and their ages at retirement.
What is the probability that a person who retired between the ages of 56 and 60 was a college professor?

A)0.274
B)0.246
C)0.068
D)0.248
E)0.275

Question 17

You draw a card at random from a standard deck of 52 cards.Find the probability that the card is a diamond given that it is a queen.

A)0
B)0.5
C)0.077
D)0.25
E)0.333

Question 18

You draw a card at random from a standard deck of 52 cards.Find the probability that the card is a spade given that it is not a diamond.

A)0.333
B)0.077
C)0
D)0.5
E)0.25

Question 19

University students were given three choices of pizza toppings and asked to choose one favorite.They were also asked what year of their program they were in.The following table shows the results.

Among the students in their third year,what is the probability that a student responded "meat"?

A)0.152
B)0.050
C)0.204
D)0.10
E)0.306

Question 20

The table shows the popular votes cast in the U.S.A in the 1984 presidential election classified by region and political party.Data are in thousands,rounded to the nearest thousand.
Find the probability that a voter who lives in the Northeast voted Democrat.

A)0.406
B)0.098
C)0.558
D)0.442
E)0.241

Question 21

Opinion-polling organizations sometimes contact their respondents by sampling random telephone numbers.Assume that interviewers can now reach about 77% of Canadian households,while the percentage of those contacted who agree to cooperate with the survey is 32%.Each household,of course,is independent of the others.What is the probability that the next household on the list will be contacted but will refuse to cooperate?

A)0.177
B)0.524
C)0.246
D)0.074
E)0.156

Question 22

There is a huge pile of buttons in which 28% are black,14% are blue,20% are orange,22% are white,and the rest are clear.You close your eyes,choose a button at random,write down what colour it is,and then put it back in the pile.What is the probability that the third button you choose is the first one that's clear?

A)0.004
B)0.022
C)0.113
D)0.593
E)0.141

Question 23

Opinion-polling organizations sometimes contact their respondents by sampling random telephone numbers.Assume that interviewers can now reach about 74% of Canadian households,while the percentage of those contacted who agree to cooperate with the survey is 32%.Each household,of course,is independent of the others.What is the probability of failing to contact a household or of contacting the household but not getting them to agree to the interview?

A)0.177
B)0.823
C)0.497
D)0.763
E)0.452

Question 24

In a business class,15% of the students have never taken a statistics class,40% 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 both of your two group mates have studied at least one semester of statistics?

A)0.40
B)0.723
C)0.16
D)0.85
E)1.7

Question 25

In a business class,15% of the students have never taken a statistics class,40% 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 neither of your two group mates has studied statistics?

A)0.45
B)0.023
C)0.15
D)0.85
E)0.30

Question 26

You roll a fair die four times.What is the probability that you roll at least one 6?

A)0.482
B)0.518
C)0.167
D)0.667
E)0.0008

Question 27

A study conducted at a college shows that 70% of the school's graduates find a job in their chosen field within a year after graduation.Find the probability that 7 randomly selected graduates all find jobs in their chosen field within a year of graduating.

A)0.1000
B)0.4900
C)4.9000
D)0.9176
E)0.0824

Question 28

You roll a fair die four times.What is the probability that the numbers you roll are not all 6's?

A)0.999
B)0.0008
C)0.833
D)0.518
E)0.482

Question 29

A manufacturing process has a 74% yield,meaning that 74% of the products are acceptable and 26% are defective.If three of the products are randomly selected,find the probability that all of them are acceptable.

A)0.405
B)0.222
C)2.22
D)0.548
E)0.018

Question 30

The date is March 8,and there are 104 people in a room.What is the probability that at least one of them has a birthday today?

A)0.250
B)0.285
C)0.248
D)0.752
E)0.750

Question 31

The date is February 29.What is the fewest number of people that must be gathered together for it to be more than likely that at least one of them has a birthday today (that is,for the probability to be greater than 0.50)?

A)253
B)811
C)409
D)731
E)1013

Question 32

You roll a fair die six times.What is the probability that you roll all 5's?

A)1
B)0.00002
C)1.2
D)0.167
E)0.833

Question 33

Opinion-polling organizations sometimes contact their respondents by sampling random telephone numbers.Assume that interviewers can now reach about 78% of Canadian households,while the percentage of those contacted who agree to cooperate with the survey is 36%.Each household,of course,is independent of the others.What is the probability of obtaining an interview with the next household on the sample list?

A)0.281
B)0.079
C)0.780
D)0.499
E)0.141

Question 34

In a business class,10% 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 at least one of your two group mates has had more than one semester of statistics?

A)0.45
B)0.203
C)0.798
D)0.55
E)0.303

Question 35

An online poll asked people how likely they were to see a new movie that was coming out in the summer.There were 1246 responses.Here's how they responded:
Let's call someone who responded that they would definitely or probably see it a "likely viewer" and the other two categories,"unlikely viewer." If we select two people at random from this sample of 1246 people,what is the probability that both are likely viewers?

A)0.161
B)0.359
C)0.801
D)0.032
E)0.400

Question 36

A study conducted at a certain college shows that 61% of the school's graduates find a job in their chosen field within a year after graduation.Find the probability that among 6 randomly selected graduates,at least one finds a job in his or her chosen field within a year of graduating.

A)0.3660
B)0.9965
C)0.9485
D)0.0035
E)0.1667

Question 37

An online poll asked people how likely they were to see a new movie that was coming out in the summer.There were 1245 responses.Here's how they responded:
Let's call someone who responded that they would definitely or probably see it a "likely viewer" and the other two categories,"unlikely viewer." If we select two people at random from this sample of 1245 people,what is the probability that neither is a likely viewer?

A)0.169
B)0.066
C)0.347
D)0.589
E)0.110

Question 38

A consumer organization estimates that 32% of the households in a particular community have one television set,38% have two sets,and 16% have three or more sets.If two households are chosen at random,what is the probability that at least one has one ore more television sets?

A)0.241
B)0.986
C)0.740
D)0.020
E)0.860

Question 39

An online poll asked people how likely they were to see a new movie that was coming out in the summer.There were 1235 responses.Here's how they responded:
Let's call someone who responded that they would definitely or probably see it a "likely viewer" and the other two categories,"unlikely viewer." If we select two people at random from this sample of 1235 people,what is the probability that one is a likely viewer and one isn't?

A)0.183
B)0.297
C)0.245
D)0.149
E)0.479

Question 40

Suppose that the Canadian Red Cross says that about 45% of the Canadian population has Type O blood,40% Type A,11% Type B,and the rest Type AB.Among six donors,what is the probability that no one is Type A?

A)0.047
B)2.400
C)0.004
D)3.600
E)0.036

Question 41

The sales bin in a clothing store contains an assortment of t-shirts in different sizes.There are 4 small,7 medium,and 9 large shirts.Alan is looking for a large shirt.He starts grabbing shirts one at a time and checking the size.After he checks each shirt,he leaves it outside the bin.What is the probability that the first large shirt he finds is the third one he checks?

A)0.074
B)0.136
C)0.145
D)0.124
E)0.091

Question 42

You are dealt a hand of three cards,one at a time.Find the probability that your cards are all aces.Round your answer to five decimal places.

A)0.00018
B)0.01294
C)0.00046
D)0.17575
E)0.00025

Question 43

You are dealt a hand of three cards,one at a time.Find the probability that your cards are all diamonds.

A)0.013
B)0.231
C)0.016
D)0.750
E)0.705

Question 44

A box contains 16 batteries of which 6 are still working.Anne starts picking batteries one at a time from the box and testing them.Find the probability that she has to pick 5 batteries in order to find one that works.

A)0.007
B)0.058
C)0.001
D)12.360
E)0.029

Question 45

A bag contains 10 red chips and 9 blue chips.Two chips are selected randomly without replacement from the bag.What is the probability that the two chips are the same color?

A)0.529
B)0.474
C)0.526
D)0.500
E)0.263

Question 46

You are dealt a hand of three cards,one at a time.Find the probability that you get no kings.

A)0.315
B)0.783
C)0.787
D)0.414
E)0.118

Question 47

You are dealt a hand of three cards,one at a time.Find the probability that you get no black cards.

A)0.231
B)0.414
C)0.118
D)0.125
E)0.013

Question 48

You are dealt a hand of three cards,one at a time.Find the probability that your cards are all face cards.

A)0.025
B)0.013
C)0.012
D)0.010
E)0.250

Question 49

You are dealt a hand of three cards,one at a time.Find the probability that you have at least one red card.

A)0.882
B)0.125
C)0.118
D)0.382
E)0.875

Question 50

Among the contestants in a competition are 50 women and 29 men.If 5 winners are randomly selected,what is the probability that they are all men? Round your answer to five decimal places.

A)0.01256
B)0.05605
C)0.00527
D)0.10156
E)0.06564

Question 51

Applicants for a job first submit a written application.Based on the written applications,37% of the applicants are invited for a first interview.Of those that have a first interview,58% are rejected after the interview.What is the probability that a randomly selected applicant receives a first interview and is rejected after the interview?

A)0.1554
B)0.58
C)0.2146
D)0.95
E)0.7354

Question 52

A box contains 14 batteries of which 6 are still working.Anne starts picking batteries one at a time from the box and testing them.Find the probability that at least one of the first four works.

A)0.893
B)0.015
C)0.084
D)0.930
E)0.070

Question 53

A box contains batteries of which 48 are defective and 24 are good.You start picking batteries one at a time and testing them.What is the probability that the first four batteries you pick are all defective?

A)18.312
B)0.063
C)0.811
D)0.189
E)0.198

Question 54

A bag contains 5 red chips and 12 blue chips.Two chips are selected randomly without replacement from the bag.What is the probability that the two chips are both red?

A)0.621
B)0.250
C)0.559
D)0.441
E)0.074

Question 55

63% of students at one college drink coffee,and 16% of people who drink coffee suffer from insomnia.What is the probability that a randomly selected student drinks coffee and suffers from insomnia?

A)0.1008
B)0.6892
C)0.5292
D)0.79
E)0.16

Question 56

A Canada Revenue auditor randomly selects 3 tax returns from 55 returns of which 14 contain errors.What is the probability that she selects none of those containing errors?

A)0.014
B)0.016
C)0.414
D)0.594
E)0.406

Question 57

You are dealt a hand of three cards,one at a time.Find the probability that you get no clubs.

A)0.783
B)0.315
C)0.414
D)0.422
E)0.118

Question 58

You are dealt a hand of three cards,one at a time.Find the probability that your third card is your first ace.

A)0.077
B)0.00018
C)0.068
D)0.145
E)0.127

Question 59

You are dealt a hand of three cards,one at a time.Find the probability that you have at least one queen.

A)0.217
B)0.204
C)0.068
D)0.783
E)0.213

Question 60

You are dealt a hand of three cards,one at a time.Find the probability that you have at least one face card.

A)0.447
B)0.545
C)0.553
D)0.010
E)0.423

Question 61

According to a survey conducted by an environmental organization,the probability that an eligible voter cares about environmental issues is 0.58,the probability that an eligible voter voted in the last election is 0.41 and the probability that an eligible voter both voted in the last election and cares about environmental issues is 0.27.Are caring about environmental issues and voting in the last election independent events?

A)Yes,the probability that a voter cares about environmental issues and voted in the last election is zero.
B)Yes,P(Cares for environment and Voted)= P(Cares for environment)∙ P(Voted)
C)No,41% of all voters voted in the last election,but among those who care about environmental issues 46.6% voted in the last election.
D)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.
E)No,27% both care about environmental issues and voted in the last election

Question 62

A group of volunteers for a clinical trial consists of 88 women and 90 men.20 of the women and 19 of the men have high blood pressure.Are high blood pressure and gender independent? Explain.

A)Yes;a patient with high blood pressure cannot be both male and female
B)No;
P(High blood pressure)= 0.219
P(High blood pressure| Female)= 0.227
These are not equal
C)No;
P(High blood pressure and Male)= 0.107
P(High blood pressure and Female)= 0.112
These are not equal
D)Yes;
P(High blood pressure and Male)= P(High blood pressure)∙ P(Male)
E)Yes;
P(High blood pressure| Female)= 0.227
P(High blood pressure| Male)= 0.227
These are equal.

Question 63

In one town in British Columbia,only 24% of days are sunny.A company's records indicate that on sunny days 1.8% of employees will call in sick.When it is not sunny,0.9% of employees will call in sick.What percent of employees call in sick on a randomly selected day?

A)1.8%
B)0.684%
C)0.432%
D)1.116%
E)1.35%

Question 64

In rolling a fair die twice,the events of getting a 1 on the first roll and a 5 on the second

A)Disjoint
B)Independent
C)Neither
D)Both

Question 65

The table shows the political affiliation of voters in one city and their positions on raising taxes.
Raising Taxes
Are party affiliation and position on raising taxes independent? Explain.

A)Yes;
62.5% of Conservative supporters favor raising taxes and
62.5% of NDP supporters favour raising taxes.
B)No;
P(Conservative and Favour)= 0.25
P(NDP and Favour)= 0.11
These are not equal
C)No;62.5% of Conservative supporters favour raising taxes,but only 29.7% of NDP supporters favour raising taxes.
D)Yes;a voter who favours raising taxes cannot be both a Conservative supporter and an NDP supporter.
E)No;11% of voters both favour raising taxes and are NDP supporters.

Question 66

In a small town,a certain type of laptop computer is sold at just two stores.Store A has 31% of the sales,3% of which are of defective items,and store B has 69% of the sales,5% of which are of defective items.A person receives one of these laptop computers as a gift.What is the probability it is defective?

A)0.03
B)0.022
C)0.044
D)0.04
E)0.34

Question 67

Melissa is looking for the perfect man.She claims that at her college 34% of men are smart,30% are funny,and 19% are both smart and funny.If Melissa is right,are being smart and being funny independent events?

A)Yes,no man is both smart and funny
B)Yes,overall 30% of men are funny.Among those who are smart ,30% are funny.
These are equal.
C)No,19% are both smart and funny
D)No,overall 30% of men are funny,but among those who are smart 55.9% are funny.These are not equal.
E)Yes,because P(Smart and Funny)= P(Smart)∙ P(Funny)

Question 68

In filling out a ballot for your local M.P. ,the events of voting for the Conservative candidate and voting for the Liberal candidate.

A)Disjoint
B)Independent
C)Neither
D)Both

Question 69

In one town in British Columbia,only 27% of days are sunny.A company's records indicate that on sunny days 1.8% of employees will call in sick.When it is not sunny,1.0% of employees will call in sick.Is calling in sick independent of sunshine? Explain.

A)Yes,the probability of an employees calling in sick does not depend on whether it is sunny.
B)No,it is possible for both things to happen
P(sunny and employee calls in sick)= (0.27)∙ (0.018).This is greater than zero.
C)No,the percentage calling in sick depends on whether it is sunny.
When it is sunny,1.8% call in sick.When it is not sunny,1.0% call in sick
D)No
P(sunny and employee calls in sick)= (0.27)∙ (0.018).= 0.00486
P(not sunny and employee calls in sick)= (0.73)∙ (0.01).= 0.0073
These are not equal
E)Yes,because P(sunny and employee calls in sick)= P(sunny)∙ P(employee calls in sick)

Question 70

4.5% of a population are infected with a certain disease.There is a test for the disease,however the test is not completely accurate.94% of those who have the disease will test positive.However 3.7% of those who do not have the disease will also test positive (false positives).What is the probability that any given person will test positive? Round your answer to three decimal places if necessary.

A)0.94
B)0.042
C)0.078
D)0.035
E)0.489

Question 71

Shameel has a flight to catch on Monday morning.His father will give him a ride to the airport.If it rains,the traffic will be bad and the probability that he will miss his flight is 0.04.If it doesn't rain,the probability that he will miss his flight is 0.01.The probability that it will rain on Monday is 0.28.Are rain and Shameel missing his flight independent events? Explain.

A)Yes,if it rains,he cannot both miss his flight and catch his flight
B)No,the probability of Shameel missing his flight depends on whether it rains.
P(miss flight| rain)= 0.04,P(miss flight|no rain)= 0.01
C)Yes,the probability of Shameel missing his flight does not depend on whether it rains.
P(miss flight| rain)= P(miss flight|no rain)= 0.04
D)Yes,because P(miss flight and rain)= P(miss flight)∙ P(rain)
E)No,it is possible for both things to happen
P(rain and miss flight)= 0.28 ∙ 0.04.This is greater than zero.

Question 72

In driving a car,the events of driving over the speed limit and getting a speeding ticket.

A)Disjoint
B)Independent
C)Neither
D)Both

Question 73

If you draw a card at random from a well-shuffled deck,is getting a club independent of getting a queen? Explain.

A)Yes.A card cannot be both a club and a queen.
B)No.The probability of getting a club and a queen is

.This is not zero
C)Yes.P(Club)=

;P(Club|Queen)=

D)No.P(C and Q)≠ P(C)∙ P(Q)
E)No.P(Club)=

;P(Club|Queen)=

Question 74

In rolling a fair die once,the events of getting a 3 and getting a 6

A)Disjoint
B)Independent
C)Neither
D)Both

Question 75

The table below describes the smoking habits of a group of asthma sufferers.
Is heavy smoking independent of gender?

A)No,overall 15.9% of the group are heavy smokers ,but 14.5% of the men are heavy smokers.These are not equal.
B)No,
P(male and heavy smoker)= 0.070
P(female and heavy smoker)= 0.089
These are not equal
C)Yes,because each of the joint probabilities is equal to the product of the marginal probabilities.
D)Yes,the percentage of women in each smoking category is the same as the percentage of men in each smoking category.
E)Yes,a heavy smoker cannot be both a man and a woman.

Question 76

In flipping a coin twice,the events of getting heads on the first flip and heads on the second flip

A)Disjoint
B)Independent
C)Neither
D)Both

Question 77

A high school offers these statistics:
23% of incoming students come from single-parent homes.
77% of incoming students come from two parent homes.
46% of incoming students from single parent homes eventually go on to get a college education.
56% of incoming students from two parent homes eventually go on to get a college education.
What percent of incoming students eventually go on to get a college education?

A)51%
B)10.58%
C)43.12%
D)53.7%
E)46%

Question 78

A high school offers these statistics:
27% of incoming students come from single-parent homes
45% of incoming students come from single-parent homes eventually go on to get a college education.
59% of incoming students from two-parent homes eventually go on to get a college education.
Is there any evidence that an incoming student's chances to eventually get a college education depend on whether they come from a single parent or two parent home? Explain.

A)No,the probability of going on to get a college education does not depend on whether the student comes from a single-parent or a two-parent home.
B)Yes
P(single-parent home and college education)= (0.27)∙ (0.45)
P(two-parent home and college education)= (0.73)∙ (0.59)
These are not equal
C)Yes,the probability of going on to get a college education depends on whether the student comes from a single-parent or two-parent home.
For students from single-parent homes,45% go on to get a college education.
For students from two-parent homes,59% go on to get a college education.
D)No,because P(single-parent home and college education)= P(single-parent home)∙ P(college education)
E)No,it is possible for both things to happen
P(single-parent home and college education)= (0.27)∙ (0.45).This is greater than zero.

Question 79

The sale bin in a clothing store contains an assortment of t-shirts in different sizes.There are 6 small,8 medium,and 5 large shirts.Alan is looking for a large shirt.He starts grabbing shirts one at a time and checking the size.After he checks each shirt,he leaves it outside the bin.What is the probability that at least one of the first four shirts he checks is a large?

A)0.295
B)0.117
C)0.742
D)0.705
E)0.258

Question 80

Shameel has a flight to catch on Monday morning.His father will give him a ride to the airport.If it rains,the traffic will be bad and the probability that he will miss his flight is 0.06.If it doesn't rain,the probability that he will miss his flight is 0.01.The probability that it will rain on Monday is 0.29.What is the probability that Shameel misses his flight?

A)0.0245
B)0.0071
C)0.035
D)0.0174
E)0.06