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Using all questions from quizzes and Exams

1

A Paramter is a numerical descriptive measure calculated from a sample T/F?

False

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2

Our population of interest is NCSU students. The averag I.Q. of all NCSU students is called a statistic T/F?

False

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3

A sociologist wishes to estimate the proportion of all adults in a certain region who have never married. In a random sample of 1,320 adults, 145 have never married. The Statistics involved is 0.1 T/F?

True

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4

Martial status of a person is an example of quantitative - discrete data T/F?

False

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5

Pie or Circle chart is not an appropriate graph for describing quantitative data T/F?

True

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6

Stem-and-leaf plot provides the most infromation abotu the shape of a data set T/F?

True

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7

Among 300 fatal car accidents, 135 were single-car crashes, 66 were two-car crashes, and 99 involved three or more cars. The relative frequency of fatal car accidents associated with two car crashes is 0.22 T/F?

True

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8

The mean is much larger than the median would indicate that a dataset is skewed to the right T/F?

True

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9

Median is NOT a meaure of spread T/F?

True

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10

If an exam was worth 100 points, and your score was at the 80th percentile, then 20% of the class had scores at or below your score T/F?

False

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11

Two or more events are said to be equally likely if each has got an equal chance for occurrence T/F?

True

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12

The sample space denoted by the letter S is the set of a few possible outcomes of an experiment T/F?

False

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13

What is an individual outcome in a sample space called?

A simple event

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14

Happening and not happening of any event is always disjoint (Mutually Exclusive) T/F?

True

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15

1.01 is the number could be the probabilty of an event that is almost certain to occur T/F?

False because you cannot have 101% for statistics, only 100%.

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16

Probability of happening and not happening of any event is always equal to zero T/F?

True

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17

In any (fair/unfair) coin tossing experiement, probabilty of getting a head or tail is always equal to 0.5 T/F?

False

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18

If E1 and E2 are two events, then union probability is denoted by P(E1 ∪ E2) and it is the probability that event E1 will occur or that event E2 will occur or both event E1 and event E2 will occur. T/F?

True

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19

Joint probability of two events E1 and E2 is the probability of occurrence of event E1 or event E2. T/F?

False

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20

Conditional probability of two events E1 given E2 is the probability of occurrence of event E1 given that event E2 has not already occurred. T/F?

False

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21

SCENARIO 1: Questions 21 to 27 based on this scenario.

The data below represent the amount of grams of carbohydrates in a serving of

breakfast cereal in a sample of 11 different servings. (You can use R Software)

11 15 23 29 19 22 21 20 15 25 17

1. Referring to Scenario 1, the range in the carbohydrate amounts is ________ grams.

a) 15 b) 5.10 c) 26.02 d)18

18

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22

Referring to Scenario 1, the variance of the carbohydrate amounts is ________ (grams squared).

a) 5.10 b) 18 c) 15 d) 26.02

26.02

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23

Referring to Scenario 1, the standard deviation of the carbohydrate amounts is ________ grams.

a) 18 b) 5.10 c) 26.02 d) 15

5.10

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24

Referring to Scenario 1, the first quartile of the carbohydrate amounts is ________ grams.

a) 18 b) 5.10 c) 15 d) 26.02

15

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25

Referring to Scenario 1, the third quartile of the carbohydrate amounts is ________ grams.

a) 15 b) 5.10 c) 23 d) 26.02

23

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26

Referring to Scenario 1, the interquartile range in the carbohydrate amounts is ________ grams.

a) 15 b) 18 c) 8 d) 23

8

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27

Referring to Scenario 1, the extreme values in the given data set are.

a) 25, 27 b) 11, 15 c) None of these d) 27 e) 11

None of These

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28

SCENARIO 2: The mean price of new homes from a sample of houses is $150, 000 with a standard deviation of $15, 000. The data set has a bell-shaped distribution.

Referring to Scenario 2, Between what two prices do 95% of the new homes fall?

$120, 000 and $180, 000

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29

Referring to Scenario 2, Find the approximate percentage of new homes whose prices are less than $135, 000?

16%

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30

Referring to Scenario 2, Find the approximate percentage of new homes whose prices are greater than $165, 000?

16%

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31

An experiment consists of tossing 4 unbiased coins simultaneously. The number of simple events in this experiment is

16

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32

Question 32 – 39: Find the indicated probability

A sample space consists of 80 simple events that are equally likely. What is the probability of each?

1/80

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33

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

5/6

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34

A bag contains 6 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?

3/16

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35

A 6-sided die is rolled. What is the probability of rolling a 3 or a 6?

1/3

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36

If P(A) = 12/19, find P(A^c).

7/19

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37

Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.315. Find the probability that in a given year it will not snow on January 1st in that town.

0.685

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38

In one town, 30% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats

0.09

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39

A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable.

0.343

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40

A random variable cannot be both discrete and continuous T/F?

True

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41

The number of letters in a word picked at random out of the dictionary is an example of continuous random variable. T/F?

False

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42

The time (in seconds) it takes one email to travel between a sender and receiver is an example of continuous random variable. T/F?

True

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43

The expected value for a random variable is the long – run average T/F?

True

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44

In a Binomial Probability Distribution, each trial is dependent of every other trial. T/F?

False

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45

Suppose that a random variable X can take the values {0, 1, 2} all with equal probability. Then the expected value of X is 1. T/F ?

True

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46

Suppose each shell sells for $5.00. On average, Sai sells 1.5 shells per day. However, Sai must pay $3.00 daily for the permit to sell shells. Let Y denote Sai’s daily profit. Then Y=5X-3. Then E(Y) is $4.50. T/F?

True

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47

If g(X) = 2X-5 is a linear combination of a random variable X, then Var(2X-5) = 2Var(X). T/F?

False

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48

Let X be the number of heads obtained in 40 independent tosses of a fair coin. Then X is a Binomial random variable with n=40, p=0.5. T/F?

True

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49

Suppose that you toss a fair coin with probability 0.5 a head. The probability of getting five heads in a row is less than three percent. T/F?

False

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50

Suppose that you toss a coin 5 times. Then there are 10 ways of getting 3 heads. T/F?

True

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51

The probability of observing three heads out of five tosses of a fair coin is 0.6. T/F?

False

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52

The probability of at least one head when tossing a fair coin 4 times is 0.9375. T/F?

True

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53

Suppose that X is Binomially distributed with E(X) = 5 and Var(X) = 2, then n = 10 and p = 0.5. T/F?

False

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54

A grocery store has 10 loaves of bread on its shelves, of which 7 are fresh and 3 are stale. Customers buy 4 loaves selecting them at random. The probability that 3 are fresh and 1 is stale is 0.5 T/F?

True

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55

At Meet the Firms, a recruiter is interviewing candidates for an internship. From past experience, the recruiter believes that only about 20% of the potential candidates have the necessary qualifications. Assume independence. The probability that the first suitable job candidate will be found during the fourth interview is 0.1024 T/F?

True

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56

An experiment consists of repeatedly and independently tossing a fair die until a six is obtained. Let X denote the number of throws before obtaining a six. Then E(X) =5 T/F?

True

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57

A large collection of tires has 3% defective tires. Suppose one chooses tires from this collection until he/she obtains 4 non-defective tires. Then the total number of defective tires drawn in this process has a Negative Binomial distribution with r = 4, p = 0.03. T/F?

False

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58

**Let X have a Poisson distribution with variance of 3. Then P(X=2) is 0.224 T/F?**

True

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59

The number of typos made by a student follows Poisson distribution with the rate of 1.5 typos per page. Assume that the numbers of typos on different pages are independent. The probability that there are exactly 10 typos in a 5-page paper is 0.086 T/F?

True

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60

SCENARIO 1: Questions 1 to 3 based on this scenario.

According to the October 2003 Current Population Survey, the following table summarizes probabilities for randomly selecting a full-time student in various age groups:

Age 15-17 18-24 25-34 35 or older

Probability .009 .623 .210 .158

If we randomly select a full-time student, what is the probability that he/she is 25 or older?

0.368

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61

If we randomly select a full-time student, the probability that he/she is not 18-24 years old is

0.377

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62

If we randomly select a full-time student, the probability that he/she is 18-30 years old is

Impossible to determine from information provided

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63

You pay $6 to play a game in which you roll a fair die. If you roll a 6, you get $8. If you roll a 5, you get $7. For any other number, you get $4. What are your expected net winnings?

-$0.83

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64

The probability that a person who has made a reservation for a trip on a twelve-vehicle ferry will actually, arrive and make the trip is 0.85. If to account for “no-shows” the ferry company makes 13 reservations for a particular trip, the chance that all 13 vehicles will show is about

0.12

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65

A trailer manufacturing company buys screw fasteners in boxes of 5,000. Two percent of all fasteners are unusable. The mean and standard deviation of the number x of unusable fasteners in a randomly selected box are about

(100, 9.9)

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66

Forty percent of passengers with a certain airline prefer a window seat. The probability that exactly two of the next ten person buying a ticket with this airline will prefer a window seat is about:

0.12

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67

Suppose that a poll of 18 voters is taken in a large city. The random variable x denotes the number of voters who favor a certain candidate for mayor. Suppose that 61% of all the city’s voters favor the candidate. The mean and standard deviation of x are respectively

(10.98, 2.07)

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68

If X ~ Bin(n=15, p=1/3). Find the probability P(mu - sigma < X < mu + sigma)

0.58772

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69

One in five $1 lottery tickets wins the buyer some kind of payoff. If a person buys five tickets, the probability that none will be a winning ticket is about:

0.33

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70

Consider a random variable Y with the probability density function

fY(y)=|y|/k,−1<y<3.

Fined the value of k to make f(y) a valid pdf.

5

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71

Consider a random variable X with the probability density function

fX(x)={1/10+1/5x,for1≤x≤3

The CDF of X is

(x^2 + x -2) / 10

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72

Consider a random variable X with the probability density function

fX(x)={1/10+1/5x, for1≤x≤3,

The expected value of of X is

2.133

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73

The probability distribution (pdf) of a random variable X is:

fX(x)={3/2(1−x^2), for0≤x≤1

Determine the mean of X, E(X) is

0.375

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74

The probability distribution (pdf) of a random variable X is:

fX(x)={3/2(1−x^2), for0≤x≤1

Determine the E(X2).

0.2

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75

Suppose the density of X is \n fX(x)={3x^2, for0≤x≤1 \n Find a median value of X.

1/(3 srt 2)

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76

The failure of a circuit board interrupts work by a computing system until a new board is delivered. Delivery time X is uniformly distributed over the interval of at least one but no more than five days. That is X~U[1, 5]. The probability that the delivery time is two or more days.

0.75

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77

A diameter X of a shaft produced has a normal distribution with parameters μ=1.005,σ=0.01. The shaft will meet specifications if its diameter is between 0.98 and 1.02 cm. Which percent of shafts will not meet specifications?

0.073

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78

Let X = monthly sick leave time have normal distribution with parameters μ= 200 hours and σ=20 hours. What amount of time X0 should be budgeted for sick leave so that the budget will not be exceeded with 80% probability?

216.8

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79

Let X~N(5,4).

Find P(4<X2 <16). Note: The range of X is: −∞<X<∞

0.2026

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80

Consider a Normal random variable X with E[X]=5 and Var(X) =16.

Find P(|X-5|>6).

0.1336

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81

The time x (in minutes) until an enzyme successfully catalyzes a biochemical reaction is approximated by this CDF:

FX(x)=1−e−x1.4,forx≥0.

What proportion of reactions is complete within 0.5 minutes?

0.3

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82

The number of calls to the call center has Poisson distribution with the rate λ = 4 calls per minute. What is the probability that we have to wait more than 20 seconds for the next call?

0.2676

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83

The total monthly rainfall (in inches) for a particular region can be modeled using Gamma distribution with α=2andβ=1.6. The mean and variance of the monthly rainfall.

E(X) = 3.2 and V(X) = 5.12

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84

The total monthly rainfall (in inches) for a particular region can be modeled using Gamma distribution with α=2andβ=1.6 The probability that the total monthly rainfall exceeds 5 inches.

0.181

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85

The failures of medical devices can be modeled as a Poisson process. Assume that units that fail are repaired immediately and the mean number of failures per hour is 0.0001. Let X denote the time until 4 failures occur. What is the probability that X exceed 40,000 hours ~=4.5 years?

0.433

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86

In a XYZ car company car saleswoman has to sell 1 car. She is provided with a very large (infinite for practical purposes) list of customers. She approaches customers sequentially according to the list. The probability that she makes a successful sale to any given customer is 0.2. She stops as soon as she sells the car. Suppose that all the customers behave independently of each other. Find the expected value and variance of the total number of customers the saleswoman has to approach.

E(X) = 5 and V(X) = 20

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87

In a XYZ car company car saleswoman has to sell 1 car. She is provided with a very large (infinite for practical purposes) list of customers. She approaches customers sequentially according to the list. The probability that she makes a successful sale to any given customer is 0.2. She stops as soon as she sells the car. Suppose that all the customers behave independently of each other. Given that the first 5 sales were failed sales, find the probability that there will be at least 9 more failed sales before a successful sale.

(0.8)^9

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88

When Paul plays pen and paper game against his favorite computer program, he wins with probability 0.60, loses with probability 0.10, and 30% of the games result is a draw. Assuming independence, find the probability that Paul’s first win happens when he plays his third game.

~ 0.096

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89

You pay $6 to play a game in which you roll a fair die. If you roll a 6, you get $8. If you roll a 5, you get $7. For any other number, you get $4. What are your expected net winnings?

-$0.83

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90

In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?

3*3*3*3*3

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91

When Paul plays pen and paper game against his favorite computer program, he wins with probability 0.60, loses with probability 0.10, and 30% of the games result is a draw. Assuming independence, find the probability that Paul wins at least 8 games in 12 games.

~ 0.438178

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92

Peter’s hamburger restaurant buys some hamburger patties infected with e-coli. The probability that the e-coli survives cooking at Bob’s is 0.3. If 100 patties are cooked, what is the expected number of patties which will have no living e-coli after cooking?

70

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93

Let the random variable X be the number of heads observed in 4196 tosses of a fair coin, then E(X2) is

4402653

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94

Professor Peter makes mistakes in class according to Poisson process with an average rate of 1.2 mistakes per class. What is the probability that Peter makes exactly 10 mistakes during two weeks of classes (that is, during 6 classes, since Peter teaches a MWF lecture)?

~0.0770

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95

When Paul plays pen and paper game against his favorite computer program, he wins with probability 0.60, loses with probability 0.10, and 30% of the games result is a draw. Assuming independence, find the probability that Paul’s fifth win happens when he plays his eighth game.

~0.17418

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96

When Paul plays pen and paper game against his favorite computer program, he wins with probability 0.60, loses with probability 0.10, and 30% of the games result is a draw. Assuming independence, find the probability that Paul wins 7 games, if he plays 10 games.

~ 0.21499

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97

In a region, 15% of the adult population are smokers, 0.86% are smokers with emphysema, and 0.24% are nonsmokers with emphysema. What is the probability that a person, selected at random, has emphysema?

0.0110

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98

An ABC automobile insurance company classifies each driver as a good risk, a medium risk, or a poor risk. Of those currently insured, 30% are good risks, 50% are medium risks, and 20% are poor risks. In any given year, the probability that a driver will have a traffic accident is 0.1 for a good risk, 0.3 for a medium risk, and 0.5 for a poor risk. The company announced that it will raise the insurance premiums for the drivers who either are poor risks or had a traffic accident during 2020, or both. What proportion of customers would have their premiums raised?

0.38

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99

The probability that 4 novels, 3 mathematics books and 2 stats books be arranged on a shelf if the mathematics books must be together and the novels must be together?

( 4!4!3!)/9!

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100

A college library has five copies of a certain text on reserve. Three copies (1, 2 and 3) are first printings, and the other two (4, and 5) are second printings. A student examines these books in random order, stopping only when a second printing has been selected. One possible outcome is 5, and another is 214.The number of sample points in the sample space S is

n(S) = 32

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