Deck 8: Probability

Question 1

There are 3 balls in a hat; one with the number 2 on it,one with the number 6 on it,and one with the number 8 on it.You pick a ball from the hat at random and then you flip a coin.Using a tree diagram ,obtain the sample space for the experiment.List the elements that make up the sample space.

A)2 H T,6 H T,8 H T
B)2 H,6 H,8 H
C)2 6 8 H,2 6 8 T
D)2 H,2 T,6 H,6 T,8 H,8 T

Answer 1

2 H,2 T,6 H,6 T,8 H,8 T

Question 2

Find the odds.
If the sectors are of equal size,what are the odds of spinning an A on this spinner?

A)2:6
B)3:5
C)6:2
D)4:2

Answer 2

3:5

Question 3

List the outcomes of the sample space.
A box contains 10 blue cards numbered 1 through 10.List the sample space of picking one card from the box.

A){100}
B){1,2,3,4,5,6,7,8,9,10}
C){10}
D){8}

Answer 3

{1,2,3,4,5,6,7,8,9,10}

Question 4

List the outcomes of the sample space.
A box contains 10 red cards numbered 1 through 10.List the sample space of picking one card from the box.

A){10}
B){100}
C){1,10}
D){1,2,3,4,5,6,7,8,9,10}

Question 5

Find the probability.
A sample of 4 different calculators is randomly selected from a group containing 10 that are defective and 28 that have no defects.What is the probability that at least one of the calculators is defective?

A)0.100
B)0.723
C)0.277
D)0.705

Question 6

List the outcomes of the sample space.
A group of 18 songs are assigned numbers 1 through 18.List the outcomes of sample space of the event choosing a song with a number 5 or less.

A){1,2,3,4}
B){1,2,3,4,5}
C){18}
D){1}

Question 7

Find the odds.
The probability of a person getting a job interview is 0.54.What are the odds against getting the interview?

A)54:100
B)23:54
C)1:54
D)23:27

Question 8

Find the odds.
In a certain town,20% of people commute to work by bus.If a person is selected randomly from the town,what are the odds against selecting someone who commutes by bus?

A)1:4
B)4:1
C)1:5
D)4:5

Question 9

Find the indicated probability.
In a homicide case 3 different witnesses picked the same man from a line up.The line up contained 5 men.If the identifications were made by random guesses,find the probability that all 3 witnesses would pick the same
Person.

A)0.008
B)0.0041152
C)0.04
D)0.6

Question 10

In a survey of the number of DVDs in a house, the table shows the probabilities.
Find the probability of a house having 1 or 2 DVDs.

A)0.57
B)0.83
C)0.95
D)0.38

Question 11

Find the odds.
Suppose you are playing a game of chance.If you bet $9 on a certain event,you will collect $360(including your $9 bet)if you win.Find the odds used for determining the payoff.

A)39:1
B)1:39
C)360:369
D)40:1

Question 12

Find the probability.
Samantha is taking courses in math and English.The probability of passing math is estimated at 0.4 and English at 0.6.She also estimates that the probability of passing at least one of them is 0.8.What is her probability of passing both courses?

A)0
B)0.12
C)0.2
D)0.8

Question 13

Find the probability.
The table below describes the smoking habits of a group of asthma sufferers. If one of the 1124 people is randomly selected,find the probability that the person is a man or a heavy smoker.

A)0.511
B)0.512
C)0.552
D)0.471

Question 14

List the outcomes of the sample space.
A 6-sided die is rolled.The sides contain the numbers 1,2,3,4,5,6.List the sample space of rolling one die.

A){1,2,3,4,5,6}
B){36}
C){6}
D){1,2,6}

Question 15

In a survey of the number of DVDs in a house, the table shows the probabilities.
Find the probability of a house having 3 or more DVDs.

A)0.57
B)0.83
C)0.05
D)0.38

Question 16

Find the probability.
At the Stop 'n Go tune-up and brake shop,the manager has found that an SUV will require a tune-up with a probability of 0.6,a brake job with a probability of 0.1 and both with a probability of 0.02.What is the
Probability that an SUV requires either a tune-up or a brake job?

A)0.32
B)0.7
C)0.58
D)0.68

Question 17

Find the probability.
In a batch of 8,000 clock radios 6% are defective.A sample of 9 clock radios is randomly selected without replacement from the 8,000 and tested.The entire batch will be rejected if at least one of those tested is defective.What is the probability that the entire batch will be rejected?

A)0.573
B)0.111
C)0.0600
D)0.427

Question 18

A fair die and a fair coin are tossed in succession.Find the sample space composed of equally likely events.

Question 19

Find the probability.
A study conducted at a certain college shows that 62% of the school's graduates find a job in their chosen field within a year after graduation.Find the probability that among 7 randomly selected graduates,at least one finds a job in his or her chosen field within a year of graduating.

A)0.143
B)0.999
C)0.965
D)0.620

Question 20

Find the odds.
If two fair dice are thrown,what are the odds of obtaining a sum of 7?

A)3:4
B)1:6
C)1:5
D)5:1

Question 21

Solve the problem.
The distribution of bachelor degrees conferred by a local college is listed below,by major. What is the probability that a randomly selected degree is not in Mathematics?

A)0.768
B)0.682
C)0.303
D)0.232

Question 22

Use a tree diagram to find the indicated probability.
In the town of Cheraw,a certain type of laptop computer is sold at just two stores.Store A has 38% of the sales, 4% of which are of defective items,and store B has 62% of the sales,2% 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)0.014
B)0.028
C)0.42
D)0.03

Question 23

Solve the problem.
At the Stop 'n Go tune-up and brake shop,the manager has found that an SUV will require a tune-up with a probability of 0.6,a brake job with a probability of 0.1 and both with a probability of 0.02.What is the probability that an SUV requires a tune-up but not a brake job?

A)0.02
B)0.58
C)0.68
D)0.7

Question 24

Use the tree diagram to find the requested probability.
Find P(XIA).Give your answer as a decimal and round your answer to three decimal places if necessary. a = 0.1,b = 0.9,c = 0.8,d = 0.2,e = 0.3,f = 0.7

A)0.08
B)0.073
C)0.229
D)0.8

Question 25

Determine independence. Answer Yes or No.
The table shows the political affiliation of voters in one city and their positions on stronger gun control laws. Are party affiliation and position on gun control laws independent?

A)Yes
B)No

Question 26

Solve the problem.
Of the coffee makers sold in an appliance store,4.0% have either a faulty switch or a defective cord,2.5% have a faulty switch,and 0.1% have both defects.What is the probability that a coffee maker will have a defective cord? Express the answer as a percentage.

A)4.0%
B)4.1%
C)2.6%
D)1.6%

Question 27

Find the probability.
The table lists the eight possible blood types.Also given is the percent of the U.S.population having that type. Let E be the event that a randomly selected person in the U.S.has type B blood.Let F be the event that a randomly selected person in the U.S.has RH-positive blood. Find P(E|F).

A)0.107
B)0.818
C)0.182
D)0.840

Question 28

Estimate the indicated probability.
College students were given three choices of pizza toppings and asked to choose one favorite.The following table shows the results. A randomly selected student who is a a junior or senior is also prefers veggie.Round the answer to the nearest hundredth.

A).391
B).408
C).229
D).688

Question 29

Solve the problem.
At the Stop 'n Go tune-up and brake shop,the manager has found that an SUV will require a tune-up with a probability of 0.6,a brake job with a probability of 0.1 and both with a probability of 0.02.What is the probability that an SUV requires neither type of repair?

A)0.7
B)0.32
C)0.68
D)0.58

Question 30

Estimate the indicated probability.
College students were given three choices of pizza toppings and asked to choose one favorite.The following table shows the results. A randomly selected student prefers a cheese topping.

A).342
B).124
C).329
D).364

Question 31

Estimate the indicated probability.
College students were given three choices of pizza toppings and asked to choose one favorite.The following table shows the results. A randomly selected student prefers a cheese topping.

A).139
B).048
C).460
D).345

Question 32

Find the probability.
People were given three choices of soft drinks and asked to choose one favorite.The following table shows the results. P(person is over 40 n person drinks diet cola)?

A)
B)
C)
D)

Question 33

Find the probability.
The table lists the eight possible blood types.Also given is the percent of the U.S.population having that type. ِ Let E be the event that a randomly selected person in the U.S.has type B blood.Let F be the event that a randomly selected person in the U.S.has RH-positive blood.
Find P(F|E).

A)0.818
B)0.340
C)0.720
D)0.107

Question 34

Find the probability.
The table shows the political affiliation of voters in a small midwestern town and their positions on stronger drug control laws. Find the probability that a Democrat opposes stronger drug control laws.

A)0.420
B)0.390
C)0.350
D)0.490

Question 35

Determine independence. Answer Yes or No.
A group of 25 people contains 10 brunettes,8 blondes,and 7 redheads.Of the 20 girls in the group,8 are brunettes,6 are blondes,and 6 are redheads.A person is selected at random.Are the events of being a girl and having brown hair independent?

A)Yes
B)No

Question 36

Use a tree diagram to find the indicated probability.
3.9% of a secluded island tribe are infected with a certain disease.There is a test for the disease,however the test is not completely accurate.92% of those who have the disease will test positive.However 4.4% 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)0.482
B)0.078
C)0.036
D)0.042

Question 37

From a survey involving 2,000 students at a large university,it was found that 1,300 students had classes on Monday,Wednesday,and Friday; 1,500 students had classes on Tuesday and Thursday; and 800 students had classes every day.If a student at this university is selected at random,what is the (empirical)probability that the student has classes only on Tuesday and Thursday?

Question 38

In a survey of the number of DVDs in a house, the table shows the probabilities.
Find the probability of a house having fewer than 2 DVDs.

A)0.71
B)0.29
C)0.57
D)0.38

Question 39

Solve the problem.
A drug company is running trials on a new test for anabolic steroids.The company uses the test on 400 athletes know to be suing steroids and 200 athletes known not to be using steroids.Of those using steroids,the new test is positive for 390 and negative for 10.Of those not using steroids,the test is positive for 10 and negative for 190.What is the estimated probability of a false negative result (the probability that an athlete using steroids will test negative)?

A)0.975
B)0.05
C)0.95
D)0.025

Question 40

Determine independence. Answer Yes or No.
According to a survey,8% of students at a college are left handed,53% are female,and 4.24% are both female and left handed.Is being left handed independent of gender?

A)Yes
B)No

Question 41

Find the expected value.
A new light bulb has been found to have a 0.02 probability of being defective.A shop owner receives 500 bulbs of this kind.How many of these bulbs are expected to be defective?

A)10
B)100
C)20
D)500

Question 42

Find the expected value.
A car agency has found daily demand to be as shown in the table. Find the expected number of customers.

A)2
B)12
C)9
D)10

Question 43

Use Bayes' rule to find the indicated probability.
An water well is to be drilled in the desert where the soil is either rock,clay or sand.The probability of rock P(R)= 0.53.The clay probability is P(C)= 0.21.The sand probability is P(S)= 0.26.It if it rock,a geological test gives a positive result with 35% accuracy.If it is clay,this test gives a positive result with 48% accuracy.The test gives a 75% accuracy for sand.Given the test is positive,what is the probability that soil is rock,P(rock | positive)?

A)P(rock | positive)= 0.209
B)P(rock | positive)= 0.405
C)P(rock | positive)= 0.53
D)P(rock | positive)= 0.385

Question 44

Use Bayes' rule to find the indicated probability.
The incidence of a certain disease on the island of Tukow is 4%.A new test has been developed to diagnose the disease.Using this test,91% of those who have the disease test positive while 4% of those who do not have the disease test positive (false positive).If a person tests positive,what is the probability that he or she actually has the disease?

A)0.438
B)0.91
C)0.487
D)0.856

Question 45

Find the expected value.
A fair coin is tossed three times,and a player wins $3 if 3 tails occur,wins $2 if 2 tails occur and loses $3 if no tails occur.If one tail occurs,no one wins.What is the expected value of the games?

A)$2.00
B)-$3.00
C)$3.00
D)$0.75

Question 46

Use Bayes' rule to find the indicated probability.
Two stores sell a certain MP3 players.Store A has 34% of the sales,5% of which are of defective items,and store B has 66% of the sales,1% of which are of defective items.The difference in defective rates is due to different levels of pre-sale checking of the product.A person receives a defective item of this product as a gift.What is the probability it came from store B?

A)0.22
B)0.7083
C)0.275
D)0.5667

Question 47

Refer to the table below for events in a sample space,S,compute P(C|E).

Question 48

Use Bayes' rule to find the indicated probability.
An water well is to be drilled in the desert where the soil is either rock,clay or sand.The probability of rock P(R)= 0.53.The clay probability is P(C)= 0.21.The sand probability is P(S)= 0.26.It if it rock,a geological test gives a positive result with 35% accuracy.If it is clay,this test gives a positive result with 48% accuracy.The test gives a 75% accuracy for sand.Given the test is positive,what is the probability that soil is rock,P(sand | positive)?

A)P(sand | positive)= 0.405
B)P(sand | positive)= 0.385
C)P(sand | positive)= 0.26
D)P(sand | positive)= 0.209

Question 49

Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the probability.
Three coins are tossed,and the number of heads is noted.

A)
B)
C)
D)

Question 50

Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the probability.
Two marbles are drawn from a bag in which there are 4 red marble and 2 blue marble.The number of blue marbles is counted.

A)
B)
C)
D)

Question 51

Use Bayes' rule to find the indicated probability.
In Cumberland County,55% of registered voters are Democrats,30% are Republicans and 15% are independent. During a recent election,35% of the Democrats voted,65% of the Republicans voted,and 75% of the
Independent voted.What is the probability that someone who voted is a Democrat?

A)0.615
B)0.55
C)0.45
D)0.385

Question 52

A calculator requires a keystroke assembly and a logic circuit.Assume that 91% of the keystroke assemblies and 93% of the logic circuits are satisfactory.Find the probability that a finished calculator will be satisfactory.
Assume that defects in keystroke assemblies are independent of defects in logic circuits.

A).8649
B).9200
C).8463
D).8281

Question 53

Use Bayes' rule to find the indicated probability.
Quality Motors has three plants.Plant 1 produces 35% of the car output,plant 2 produces 20% and plant 3 produces the remaining 45%.One percent of the output of plant 1 is defective,1.8% of the output of plant 2 is defective and 2% of the output of plant 3 is defective.The annual total production of Quality Motors is 1,000,000 cars.A car chosen at random from the annual output and is found defection.What is the probability that it came from plant 2?

A)0.217
B)0.35
C)0.559
D)0.224

Question 54

Use Bayes' rule to find the indicated probability.
Two shipments of components were received by a factory and stored in two separate bins.Shipment I has 2% of its contents defective,while shipment II has 5% of its contents defective.If it is equally likely an employee will go to either bin and select a component randomly,what is the probability that a defective component came from shipment II?

A)0.5
B)0.333
C)0.714
D)0.25

Question 55

If 82% of scheduled flights actually take place and cancellations are independent events,what is the probability that 3 separate flights will all take place?

A).82
B).55
C).01
D).67

Question 56

Use Bayes' rule to find the indicated probability.
An water well is to be drilled in the desert where the soil is either rock,clay or sand.The probability of rock P(R)= 0.53.The clay probability is P(C)= 0.21.The sand probability is P(S)= 0.26.It if it rock,a geological test gives a positive result with 35% accuracy.If it is clay,this test gives a positive result with 48% accuracy.The test gives a 75% accuracy for sand.Given the test is positive,what is the probability that soil is clay,P(clay | positive)?

A)P(clay | positive)= 0.53
B)P(clay | positive)= 0.209
C)P(clay | positive)= 0.385
D)P(clay | positive)= 0.405

Question 57

Use Bayes' rule to find the indicated probability.
In Cumberland County,55% of registered voters are Democrats,30% are Republicans and 15% are independent. During a recent election,35% of the Democrats voted,65% of the Republicans voted,and 75% of the Independent voted.What is the probability that someone who voted is a Republican?

A)0.225
B)0.39
C)0.065
D)0.385

Question 58

Find the expected value.
Suppose that 1,000 tickets are sold for a raffle that has the following prizes: one $300 prize,two $100 prizes,and one hundred $1 prizes.What is expected value of a ticket?

A)$1
B)$100
C)$0.60
D)$300

Question 59

Provide an appropriate response.
In a raffle 1000 tickets are being sold at $1.00 each.The first prize is $100,and there are 3 second prizes fo $50 each.By how much does the price of a ticket exceed its expected value?

A)$1.75
B)$50
C)$0.75
D)$1.00

Question 60

Use the tree diagram to find the requested probability.
Find P(XIA).Give your answer as a decimal and round your answer to three decimal places if necessary. a = 0.7,b = 0.3,c = 0.1,d = 0.9,e = 0.2,f = 0.8

A)0.1
B)0.233
C)0.538
D)0.07

Question 61

Find the expected value.
Mr.Cameron is sponsoring an summer concert.He estimates that he will make $300,000 if it does not rain and make $60,000 if it does rain.The weather bureau predicts the chance of rain is 0.34 for the day of the concert.What are Mr.Cameron's expected concert earning?

A)$360,000
B)$60,000
C)$300,000
D)$218,400

Question 62

Provide an appropriate response.
The probability distribution for the random variable X is: What is the expected value of X?

A)0.62
B)0.50
C)0.22
D)0.26

Question 63

A shipment of 20 digital cameras contains two that are defective.A random sample of three is selected and tested.Let X be the random variable associated with the number of defective cameras in a sample.Find the probability distribution of X and the expected number of defective cameras in a sample.

Question 64

Provide an appropriate response.
The number of loaves of whole wheat bread left on the shelf of a local quick stop at closing (denoted by the random variable X)varies from day to day.Past records show that the probability distribution of X is as shown in the following table.Find the probability that there will be at least three loaves left over at the end of any given day.

A)0.15
B)0.65
C)0.20
D)0.35

Question 65

Find the expected value.
Mr.Cameron is sponsoring an summer concert.He estimates that he will make $300,000 if it does not rain and make $60,000 if it does rain.The weather bureau predicts the chance of rain is 0.34 for the day of the concert.An insurance company is willing to insure the concert for $150,000 against rain for a premium of $30,000.If he buys this policy,what are his expected earnings from the concert?

A)$239,400
B)$180,000
C)$300,000
D)$270,000