Question 1

We draw a card from a deck 6 times (replacing the card after each draw)and get 3 kings.How likely is this?

Accepted Answer

A) Yes. 
B) No.More than two outcomes are possible. 
C) No.The chance of getting a king changes as cards are drawn. 
D) No.6 is more than 10% of 52 
E) No.The draws are not independent of each other. 
A) Yes. 
B) No.More than two outcomes are possible. 
C) No.The chance of getting a king changes as cards are drawn. 
D) No.6 is more than 10% of 52 
E) No.The draws are not independent of each other.

Question 2

An archer is able to hit the bull's eye 65% of the time.If she keeps shooting arrows until she hits the bull's-eye,how long do you expect it will take? Assume each shot is independent of the others.

Accepted Answer

A) 2.86 shots 
B) 0.35 shots 
C) 1.54 shots 
D) 0.65 shots 
E) 65 shots 
A) 2.86 shots 
B) 0.35 shots 
C) 1.54 shots 
D) 0.65 shots 
E) 65 shots

Question 3

A tennis player usually makes a successful first serve 74% of the time.She buys a new racket hoping that it will improve her success rate.During the first month of playing with her new racket she makes 402 successful first serves out of 500.Is this evidence that with the new racket her success rate has improved? In other words,is this an unusual result for her? Explain.

Accepted Answer

A) No;we would normally expect her to make 370 first serves with a standard deviation of 19.24.402 is 1.7 standard deviations above the expected value.That's not an unusual result. 
B) No;we would normally expect her to make 370 first serves with a standard deviation of 96.20.402 is 0.3 standard deviations above the expected value.That's not an unusual result. 
C) No;we would normally expect her to make 370 first serves with a standard deviation of 9.81.402 is 3.3 standard deviations above the expected value.That's not an unusual result. 
D) Yes;we would normally expect her to make 370 first serves with a standard deviation of 96.20.402 is 0.3 standard deviations above the expected value.That's an unusual result. 
E) Yes;we would normally expect her to make 370 first serves with a standard deviation of 9.81.402 is 3.3 standard deviations above the expected value.That's an unusual result. 
A) No;we would normally expect her to make 370 first serves with a standard deviation of 19.24.402 is 1.7 standard deviations above the expected value.That's not an unusual result. 
B) No;we would normally expect her to make 370 first serves with a standard deviation of 96.20.402 is 0.3 standard deviations above the expected value.That's not an unusual result. 
C) No;we would normally expect her to make 370 first serves with a standard deviation of 9.81.402 is 3.3 standard deviations above the expected value.That's not an unusual result. 
D) Yes;we would normally expect her to make 370 first serves with a standard deviation of 96.20.402 is 0.3 standard deviations above the expected value.That's an unusual result. 
E) Yes;we would normally expect her to make 370 first serves with a standard deviation of 9.81.402 is 3.3 standard deviations above the expected value.That's an unusual result.

Question 4

Find the probability of at least 2 girls in 10 births.Assume that male and female births are equally likely and that the births are independent events.

Accepted Answer

A) 0.989 
B) 0.011 
C) 0.044 
D) 0.1 
E) 0.945 
A) 0.989 
B) 0.011 
C) 0.044 
D) 0.1 
E) 0.945

Question 5

Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presale testing.If you test 3 chips,what is the probability that none of the chips fail?

Accepted Answer

A) 0.97 
B) 0.03 
C) 2.7 ×
  
D) 0.09 
E) 0.9127 
A) 0.97 
B) 0.03 
C) 2.7 ×
  
D) 0.09 
E) 0.9127

Question 6

Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presale testing.If you test 4 chips,what is the probability that all of the chips fail?

Accepted Answer

A) 0.03 
B) 0.08853 
C) 0.97 
D) 8.1 ×
  
E) 0.12 
A) 0.03 
B) 0.08853 
C) 0.97 
D) 8.1 ×
  
E) 0.12

Question 7

For a certain type of fabric,the average number of defects in each square foot of fabric is 0.9.Find the probability that a randomly selected square foot of the fabric will contain more than one defect.

Accepted Answer

A) 0.5934 
B) 0.2275 
C) 0.6341 
D) 0.7725 
E) 0.1647 
A) 0.5934 
B) 0.2275 
C) 0.6341 
D) 0.7725 
E) 0.1647

Question 8

A hair salon claims that 90% of their customers are satisfied.However,Toni who recently started working there found that of 120 customers last week,only 100 were satisfied.If it were true that on average 90% of customers are satisfied,what is the chance that among 120 customers 100 or fewer would be satisfied?

Accepted Answer

A) 0.2297 
B) 0.9925 
C) 0.7703 
D) 0.0075 
E) 0.0003 
A) 0.2297 
B) 0.9925 
C) 0.7703 
D) 0.0075 
E) 0.0003

Question 9

The probability that a car will have a flat tire while driving through a certain tunnel is 0.00006.Use the Poisson approximation to the binomial distribution to find the probability that among 13,000 cars passing through this tunnel,at most two will have a flat tire.

Accepted Answer

A) 0.1394 
B) 0.1840 
C) 0.9554 
D) 0.8160 
E) 0.8606 
A) 0.1394 
B) 0.1840 
C) 0.9554 
D) 0.8160 
E) 0.8606

Question 10

Bill claims that he has a coin which is biased and which comes up heads more than tails.His claim is based on a trial in which he flipped the coin 200 times and got 110 heads.If the coin were actually fair,what would be the probability of getting 110 or more heads?

Accepted Answer

A) 0.579 
B) 0.421 
C) 0.079 
D) 0.059 
E) 0.921 
A) 0.579 
B) 0.421 
C) 0.079 
D) 0.059 
E) 0.921

Question 11

Suppose a computer chip manufacturer rejects 15% of the chips produced because they fail presale testing.If you test 3 chips,what is the probability that not all of the chips fail?

Accepted Answer

A) 0.45 
B) 0.9966 
C) 0.6141 
D) 3.375 ×
  
E) 0.15 
A) 0.45 
B) 0.9966 
C) 0.6141 
D) 3.375 ×
  
E) 0.15

Question 12

We draw a card from a deck 40 times to find the distribution of the suits.After each draw the card is replaced.

Accepted Answer

A) Yes. 
B) No.More than two outcomes are possible. 
C) No.The draws are not independent of each other. 
D) No.40 is more than 10% of 52 
E) No.The chance of getting each suit changes from one draw to the next. 
A) Yes. 
B) No.More than two outcomes are possible. 
C) No.The draws are not independent of each other. 
D) No.40 is more than 10% of 52 
E) No.The chance of getting each suit changes from one draw to the next.

Question 13

A tennis player makes a successful first serve 60% of the time.If she serves 25 times,what is the mean of the number of good first serves? Assume that each serve is independent of the others.

Accepted Answer

A) 15 
B) 10 
C) 6.00 
D) 12.5 
E) 2.45 
A) 15 
B) 10 
C) 6.00 
D) 12.5 
E) 2.45

Question 14

Suppose a computer chip manufacturer rejects 5% of the chips produced because they fail presale testing.If we select 50 chips at random,how many chips do you expect to fail the testing?

Accepted Answer

A) 0.05 chips 
B) 21.8 chips 
C) 2.5 chips 
D) 5 chips 
E) 2 chips 
A) 0.05 chips 
B) 21.8 chips 
C) 2.5 chips 
D) 5 chips 
E) 2 chips

Question 15

A test consists of 10 true/false questions.If a student guesses on each question,what is the probability that the student will answer at least 6 questions correctly.

Accepted Answer

A) 0.172 
B) 0.205 
C) 0.828 
D) 0.377 
E) 0.6 
A) 0.172 
B) 0.205 
C) 0.828 
D) 0.377 
E) 0.6

Question 16

An archer is able to hit the bull's eye 77% of the time.If she shoots 6 arrows,what is the standard deviation of the number of bull's-eyes that she gets? Assume the shots are independent of each other.

Accepted Answer

A) 1.38 
B) 3 
C) 4.62 
D) 1.03 
E) 1.0626 
A) 1.38 
B) 3 
C) 4.62 
D) 1.03 
E) 1.0626

Question 17

A tennis player makes a successful first serve 65% of the time.Assume that each serve is independent of the others.If she serves 5 times,what is the probability that she makes all of her first serves?

Accepted Answer

A) 0.175 
B) 0.0053 
C) 0.1160 
D) 0.65 
E) 0.325 
A) 0.175 
B) 0.0053 
C) 0.1160 
D) 0.65 
E) 0.325

Question 18

In a study,38% of adults questioned reported that their health was excellent.A researcher wishes to study the health of people living close to a nuclear power plant.Among 10 adults randomly selected from this area,only 3 reported that their health was excellent.Find the probability that when 10 adults are randomly selected,3 or fewer are in excellent health.

Accepted Answer

A) 0.4336 
B) 0.3093 
C) 0.2017 
D) 0.5664 
E) 0.2319 
A) 0.4336 
B) 0.3093 
C) 0.2017 
D) 0.5664 
E) 0.2319

Question 19

A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 20 components and accept the whole batch if there are fewer than 3 defectives.If a particular shipment of thousands of components actually has a 4% rate of defects,what is the probability that this whole shipment will be accepted?

Accepted Answer

A) 0.9561 
B) 0.0439 
C) 0.0364 
D) 0.5141 
E) 0.1458 
A) 0.9561 
B) 0.0439 
C) 0.0364 
D) 0.5141 
E) 0.1458

Question 20

In one city,the probability that a person will pass his or her driving test on the first attempt is 0.68.11 people are selected at random from among those taking their driving test for the first time.What is the probability that among these 11 people,the number passing the test is between 2 and 4 inclusive?

Accepted Answer

A) 0.0057 
B) 0.0345 
C) 0.0299 
D) 0.0251 
E) 0.0308 
A) 0.0057 
B) 0.0345 
C) 0.0299 
D) 0.0251 
E) 0.0308

Exam 16: Probability Models

We draw a card from a deck 6 times (replacing the card after each draw)and get 3 kings.How likely is this?

An archer is able to hit the bull's eye 65% of the time.If she keeps shooting arrows until she hits the bull's-eye,how long do you expect it will take? Assume each shot is independent of the others.

Find the probability of at least 2 girls in 10 births.Assume that male and female births are equally likely and that the births are independent events.

Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presale testing.If you test 3 chips,what is the probability that none of the chips fail?

Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presale testing.If you test 4 chips,what is the probability that all of the chips fail?

For a certain type of fabric,the average number of defects in each square foot of fabric is 0.9.Find the probability that a randomly selected square foot of the fabric will contain more than one defect.

The probability that a car will have a flat tire while driving through a certain tunnel is 0.00006.Use the Poisson approximation to the binomial distribution to find the probability that among 13,000 cars passing through this tunnel,at most two will have a flat tire.

Bill claims that he has a coin which is biased and which comes up heads more than tails.His claim is based on a trial in which he flipped the coin 200 times and got 110 heads.If the coin were actually fair,what would be the probability of getting 110 or more heads?

Suppose a computer chip manufacturer rejects 15% of the chips produced because they fail presale testing.If you test 3 chips,what is the probability that not all of the chips fail?

We draw a card from a deck 40 times to find the distribution of the suits.After each draw the card is replaced.

A tennis player makes a successful first serve 60% of the time.If she serves 25 times,what is the mean of the number of good first serves? Assume that each serve is independent of the others.

Suppose a computer chip manufacturer rejects 5% of the chips produced because they fail presale testing.If we select 50 chips at random,how many chips do you expect to fail the testing?

A test consists of 10 true/false questions.If a student guesses on each question,what is the probability that the student will answer at least 6 questions correctly.

An archer is able to hit the bull's eye 77% of the time.If she shoots 6 arrows,what is the standard deviation of the number of bull's-eyes that she gets? Assume the shots are independent of each other.

A tennis player makes a successful first serve 65% of the time.Assume that each serve is independent of the others.If she serves 5 times,what is the probability that she makes all of her first serves?

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Understanding and Comparing Distributions

The Standard Deviation As a Ruler and the Normal Model

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Re-Expressing Data: Get It Straight

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From Randomness to Probability

Probability Rules

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Testing Hypotheses About Proportions

More About Tests

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