Question 1

Event A has probability 0.4. Event B has probability 0.5. A third event, C, has probability 0.6. Which of the following must be true?

Accepted Answer

C must have some elements in common with at least one of A or B

Question 2

The probability density of a random variable X is given in the following figure. From this density, the probability that X is between 0.5 and 1.5 is

Accepted Answer

1/2

Question 3

Suppose X is a continuous random variable taking values between 0 and 2 and having the following probability density function. P(1 X 2) has value

Accepted Answer

0.50

Question 4

All human blood can be typed as one of O, A, B, or AB. The distribution of the types varies a bit with race. Choose an African American person at random. Here are the approximate probabilities that the person you choose will have blood type O, B, or AB. The probability that the person chosen has a blood type other than O is

Accepted Answer

0.50

Question 5

A physician observes the number of lesions on subjects who had regularly used tanning salons. Let X be the number of lesions observed. The physician found that X had the following probability distribution. The probability that a randomly chosen subject has at least three lesions is

Accepted Answer

0.6.

Question 6

For homework in a statistics course, you are asked to flip a coin 100 times and to keep track of the number of heads. In the first 50 flips, you get 20 heads. Assume the coin is fair, that is, the probability of heads is Â½ and the probability of tails is Â½.

Accepted Answer

the proportion of times this event will occur in a very long series of repetitions.

Question 7

Some argue that millions of Americans are so hooked on television that their viewing habits fit the criteria for substance abuse as defined in the official psychiatric manual. Choose a young person (aged 19 to 25) at random and ask, \"In the past seven days, how many days did you watch television?\" Call the response X for short. Here is a probability model for the response: The probability that a randomly selected student did not watch TV 7 days in the past week is

Accepted Answer

0.43

Question 8

The Centers for Disease Control and Prevention reports that the rate of Chlamydia infections among American women ages 20 to 24 is 2791.5 per 100,000. The risk of a Chlamydia infection in the 20- to 24-year-old U.S. female population is approximately

Accepted Answer

0.0279

Question 9

Suppose we have a loaded die which gives the outcomes 1 through 6 according to the following probability distribution. Note that for this die all outcomes are not equally likely as they would be if this were a fair die.  If this die is rolled 6000 times, the number of times we get a 2 or a 3 should be about

Accepted Answer

3000

Question 10

A valid probability is any number between -1 and 1.

Accepted Answer

False

Question 11

Which of the following is (are) appropriate statements about randomness and/or probability?

Accepted Answer

All of the above are appropriate statements

Question 12

If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. Assume the table below gives the probabilities for the color of a randomly chosen M&M: What is the probability of not drawing a red candy?

Accepted Answer

0.7

Question 13

A standard deck of cards has 52 cards. The cards have one of 2 colors: 26 cards in the deck are red and 26 are black. The cards have one of 4 denominations: 13 cards are hearts (red), 13 cards are diamonds (red), 13 cards are clubs (black), and 13 cards are spades (black). Two cards are selected at random and the color is recorded. Which of the following is the correct sample space S for the set of possible outcomes?

Accepted Answer

S = {(red, red), (red, black), (black, red), (black, black)

Question 14

If two events have no outcomes in common, then those two events are ________.

Accepted Answer

disjoint

Question 15

Ignoring twins and other multiple births, assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. Define events A = {the next two babies are boys} and B = {at least one of the next two babies is a boy}. What do we know about events A and B?

Accepted Answer

None of the above.

Question 16

The probability density of a random variable X is given in the following figure. The median of the distribution of X is

Accepted Answer

1

Question 17

The frequency of color blindness (dyschromatopsia) in the Caucasian American male population is estimated to be about 8%. Let\'s call X the number of color blind individuals in a random sample of 8 Caucasian American males. The table below gives the probability distribution for X: What is the probability of getting at least 6 color blind individuals in the sample?

Accepted Answer

. 0.000

Question 18

The following is a probability distribution for the number of seeds produced by a plant. Which of the following is correct?

Accepted Answer

The probability of a plant producing three seeds or less is 0.5

Question 19

The Centers for Disease Control and Prevention reports that the rate of Chlamydia infections among American women ages 20 to 24 is 2791.5 per 100,000. The probability that a randomly chosen American woman between the ages of 20 and 24 does not have a Chlamydia infection is

Accepted Answer

0.9721

Question 20

Some argue that millions of Americans are so hooked on television that their viewing habits fit the criteria for substance abuse as defined in the official psychiatric manual. Choose a young person (aged 19 to 25) at random and ask, \"In the past seven days, how many days did you watch television?\" Call the response X for short. Here is a probability model for the response: For a randomly selected student, the events X = 3 and X = 4 are

Accepted Answer

disjoint

Question 21

For homework in a statistics course, you are asked to flip a coin 100 times and to keep track of the number of heads. In the first 50 flips, you get 20 heads. Assume the coin is fair, that is, the probability of heads is Â½ and the probability of tails is Â½. To say that the coin is \"fair\" means that, when I toss it, each of the outcomes H and T have a probability Â½ of occurring. This means that

Accepted Answer

None of the above

Question 22

The odds of becoming pregnant during regular intercourse without prophylactics are about 1/5. Which of the following is correct?

Accepted Answer

The probability of becoming pregnant is 0.16

Question 23

Many health professionals believe that attention disorders such as ADD and ADHD are being over-diagnosed. It is predicted that 60% of the diagnoses are incorrect. What is the odds of a diagnosis being incorrect?

Accepted Answer

1.50

Question 24

Suppose we toss a penny and a nickel. Let A be the event that the penny is a head and B be the event that the nickel is a tail. The events A and B are

Accepted Answer

independent.

Question 25

A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 2 mangos. Imagine you stick your hand into the refrigerator and pull out a piece of fruit at random. What is the probability you pick a plum?

Accepted Answer

1/4

Question 26

A penny is tossed. We observe whether it lands heads up or tails up. Suppose the penny is a fair coin, i.e., the probability of heads is 0.5 and the probability of tails is 0.5. What does this mean?

Accepted Answer

If the coin is tossed many, many times, the proportion of tosses that land heads will be approximately , and this proportion will tend to get closer and closer to as the number of tosses increases

Question 27

A study was conducted in a large population of adults concerning eyeglasses for correcting reading vision. Based on an examination by a qualified professional, the individuals were judged as to whether or not they needed to wear glasses for reading. In addition it was determined whether or not they were currently using glasses for reading. The following table provides the proportions found in the study: If a single adult is selected at random from this large population, what is the probability that the adult is judged to need eyeglasses for reading?

Accepted Answer

0.60

Question 28

The statistics of a particular basketball player state that he makes 4 out of 5 free-throw attempts. The basketball player is just about to attempt a free throw. What do you estimate the probability that the player makes this next free throw to be?

Accepted Answer

0.80

Question 29

If you draw an M;M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. Assume the table below gives the probabilities for the color of a randomly chosen M;M: What is the probability that you draw neither a brown nor a green candy?

Accepted Answer

0.6

Question 30

The density curve for a continuous random variable X has which of the following properties?

Accepted Answer

all of the above

Question 31

For homework in a statistics course, you are asked to flip a coin 100 times and to keep track of the number of heads. In the first 50 flips, you get 20 heads. Assume the coin is fair, that is, the probability of heads is Â½ and the probability of tails is Â½. In the next 50 flips, which of the following must happen?

Accepted Answer

None of the above

Question 32

If you draw an M;M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. The following table gives the probability that a randomly chosen M;M has each color. (These probabilities came from the M;M\'s website.) The probability that I do not draw a red candy is

Accepted Answer

0.87

Question 33

For homework in a statistics course, you are asked to flip a coin 100 times and to keep track of the number of heads. In the first 50 flips, you get 20 heads. Assume the coin is fair, that is, the probability of heads is Â½ and the probability of tails is Â½.

Accepted Answer

the proportion of times this event will occur in a very long series of repetitions.

Question 34

Rabies is a viral disease of mammals transmitted through the bite of a rabid animal. The virus infects the central nervous system, causing encephalopathy and ultimately death. The Florida Department of Health reports the distribution of documented cases of rabies for all of 2009:

Accepted Answer

The probability of a documented case of rabies in raccoons or foxes is 0.74

Question 35

The Centers for Disease Control and Prevention receives information about the causes for HIV/AIDS infection in the United States. Here are the causes of infection and their respective probability among American women ages 20 to 24 years old. This is a legitimate probability model. Therefore, the probability that an American woman age 20 to 24 was infected via injection drug use is

Accepted Answer

0.116

Question 36

A study was conducted in a large population of adults concerning eyeglasses for correcting reading vision. Based on an examination by a qualified professional, the individuals were judged as to whether or not they needed to wear glasses for reading. In addition it was determined whether or not they were currently using glasses for reading. The following table provides the proportions found in the study: Suppose two adults are selected from the population independently and at random. What is the probability that both were judged to need eyeglasses and neither was using them for reading?

Accepted Answer

0.0324

Question 37

Belgium has two official languagesâFrench and Dutch. Assume that about 60% of the people speak Dutch and 40% of the people speak French. Define the event A as the event that two randomly selected Belgians speak the same language. What is the complement of event A?

Accepted Answer

{(Dutch, French), (French, Dutch)}

Question 38

Two events are considered independent if the outcome of one does not influence the outcome of the other?

Accepted Answer

true

Question 39

A standard deck of cards has 52 cards. The cards have one of 2 colors: 26 cards in the deck are red and 26 are black. The cards have one of 4 denominations: 13 cards are hearts (red), 13 cards are diamonds (red), 13 cards are clubs (black), and 13 cards are spades (black). Two cards are selected at random. Event C is defined as the event that the first card is clubs, event R as the event that the first card is red, and event B as the event that the second card is black. Which events are disjoint?

Accepted Answer

R and C only.

Question 40

A study was conducted in a large population of adults concerning eyeglasses for correcting reading vision. Based on an examination by a qualified professional, the individuals were judged as to whether or not they needed to wear glasses for reading. In addition it was determined whether or not they were currently using glasses for reading. The following table What is the probability that the selected adult is judged to need eyeglasses but does not use them for reading?

Accepted Answer

0.18

Question 41

The statistics of a particular basketball player state that he makes 4 out of 5 free-throw attempts. During a season, the basketball player makes an average of about 200 free-throw attempts. On how many of these throws would you estimate he will actually score a point?

Accepted Answer

160

Question 42

The chances of being infected with a common cold are about 1/3 after being sneezed upon by an infected person. If you take vitamin C, the odds of catching cold after being sneezed upon are cut in half. Which of the following is correct?

Accepted Answer

The odds of catching a cold after being sneezed upon while NOT taking Vitamin C are 1:2.

Question 43

For homework in a statistics course, you are asked to flip a coin 100 times and to keep track of the number of heads. In the first 50 flips, you get 20 heads. Assume the coin is fair, that is, the probability of heads is Â½ and the probability of tails is Â½. There are only two outcomes when the coin is tossed: { H, T}. This collection of all possible outcomes is called

Accepted Answer

the sample space

Question 44

Which of the following statements is not true about continuous probability distributions?

Accepted Answer

There are no disjoint events in continuous probability models

Question 45

A researcher is trying to determine the proportion of a certain species of fish in a local lake. After sampling 40 fish, she found 32 of them were the species of interest. She estimates the probability that the next fish is of the species of interest to be

Accepted Answer

.80

Question 46

The frequency of color blindness (dyschromatopsia) in the Caucasian American male population is estimated to be about 8%. Let\'s call X the number of color blind individuals in a random sample of 8 Caucasian American males. The table below gives the probability distribution for X: Which is the correct notation for representing the probability of getting at least 4 color blind individuals in the sample?

Accepted Answer

P(X ? 4)

Question 47

Event A has probability 0.4. Event B has probability 0.5. If A and B are disjoint, then the probability of A or B is

Accepted Answer

0.9

Question 48

At the end of a production run manufacturing rubber gaskets, items are sampled at random and inspected to determine if the item is Acceptable (A), or Defective (D). Suppose it is planned to select two items and determine if each is either A or D. Which set of outcomes describes the event that at least one of the items selected is defective?

Accepted Answer

{AD, DA, DD}

Question 49

If you draw an M;M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. Assume the table below gives the probabilities for the color of a randomly chosen M;M: If you select two M;M\'s and the colors are independent, then what is the probability that both are the same color?

Accepted Answer

0.22

Question 50

A phenomenon is observed many, many times under identical conditions. The proportion of times a particular event A occurs is recorded. What does this proportion represent?

Accepted Answer

The probability of the event A.

Question 51

f you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. Assume the table below gives the probabilities for the color of a randomly chosen M&M: What is the probability of drawing a yellow candy?

Accepted Answer

0.1

Question 52

A standard deck of cards has 52 cards. The cards have one of 2 colors: 26 cards in the deck are red and 26 are black. The cards have one of 4 denominations: 13 cards are hearts (red), 13 cards are diamonds (red), 13 cards are clubs (black), and 13 cards are spades (black). Two cards are selected at random and the denomination is recorded. The event H is defined as the event that the first card is hearts. Which of the following correctly defines event H?

Accepted Answer

H = {(hearts, diamonds), (hearts, clubs), (hearts, spades), (hearts, hearts)}

Question 53

The frequency of color blindness (dyschromatopsia) in the Caucasian American male population is estimated to be about 8%. Let\'s call X the number of color blind individuals in a random sample of 8 Caucasian American males. The table below gives the probability distribution for X: What is the probability of getting exactly 4 color blind individuals in the sample?

Accepted Answer

0.002

Question 54

All human blood can be typed as one of O, A, B, or AB. The distribution of the types varies a bit with race. Choose an African American person at random. Here are the approximate probabilities that the person you choose will have blood type O, B, or AB. Considering having type AB blood to be an undesirable outcome, the odds of having type AB blood are

Accepted Answer

0.053

Question 55

The odds of a Chlamydia infection in the 20- to 24-year-old U.S. female population is approximately

Accepted Answer

.0287

Question 56

he risk of a Chlamydia infection in the 20- to 24-year-old U.S. female population is approximately

Accepted Answer

0.0279.

Question 57

What is the probability that the next three babies are of the same sex?

Accepted Answer

0.250

Question 58

A college basketball player makes 80% of his free throws. At the beginning of a game he misses his first two free throws. We may correctly conclude

Accepted Answer

Neither answer is correct.

Question 59

In a probability model, all possible outcomes together must have a probability of 1.

Accepted Answer

False

Question 60

One card is selected at random and the denomination is recorded. Which of the following is the correct sample space S for the set of possible outcomes?

Accepted Answer

S = {hearts, diamonds, clubs, spades}

Question 61

The probability that a randomly chosen American between the ages of 18 and 24 does not have myopia is

Accepted Answer

0.619

Question 62

The probability that X = 1.5 is

Accepted Answer

0.

Question 63

The following is a probability distribution for the number of seeds produced by a plant. Which of the following is correct?

Accepted Answer

The odds that a plant will produce one seed are 0.25

Question 64

At the end of a production run manufacturing rubber gaskets, items are sampled at random and inspected to determine if the item is Acceptable (A), or Defective (D). Suppose it is planned to select two items and determine if each is either A or D. What is the sample space S of the outcomes?

Accepted Answer

S = {AA, AD, DA, DD}

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