Question 1

Event A has probability 0.4. Event B has probability 0.5. If A and B are disjoint, what is the probability that both events occur?

Accepted Answer

A) 0.0 
B) 0.1 
C) 0.2 
D) 0.9 
A) 0.0 
B) 0.1 
C) 0.2 
D) 0.9 A

Question 2

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 are the odds of a diagnosis being incorrect?

Accepted Answer

A) 0.40 
B) 0.60 
C) 0.67 
D) 1.50 
A) 0.40 
B) 0.60 
C) 0.67 
D) 1.50 D

Question 3

All human blood can be typed as either 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:
?
$$\begin{array} { | l | l | l | l | l | } 
\hline \text { Blood type } & \text { O } & \text { A } & \text { B } & \text { AB } \
\hline \text { Probability } & 0.50 & ? & 0.20 & 0.05 \
\hline
\end{array}$$ What is the probability that the person chosen has a blood type other than O?

Accepted Answer

A) 0.25 
B) 0.50 
C) 0.75 
D) 1.00 
A) 0.25 
B) 0.50 
C) 0.75 
D) 1.00 B

Question 4

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 gives the probability distribution for X.
?
?
$$\begin{array} { | l | l | l | l | l | l | l | l | l | l | } 
\hline X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \
\hline P ( X ) & 0.513 & 0.357 & 0.109 & 0.019 & 0.002 & 0.000 & 0.000 & 0.000 & 0.000 \
\hline
\end{array}$$ What is the standard deviation of this distribution?

Accepted Answer

A) 0.64 
B) 0.766 
C) 0.096 
D) None of these choices is correct. 
A) 0.64 
B) 0.766 
C) 0.096 
D) None of these choices is correct.

Question 5

An odds is the ratio of the probability of an outcome over the probability of that outcome not
occurring.

Accepted Answer

A) True 
 B)False

Question 6

Based on a recent Gallup survey, we define the following probability model for the number X of daily cups of coffee consumed by Americans.
​
​
 $$\begin{array} { | l | l | l | l | l | l | } 
\hline X & 0 & 1 & 2 & 3 & 4 \text { or more } \
\hline \text { Probability } & 0.36 & 0.26 & 0.19 & 0.09 & ? \
\hline
\end{array}$$ What is the probability that an American consumes at most 1 cup of coffee daily?

Accepted Answer

The answer of Based on a recent Gallup survey, we...

Question 7

Event A occurs with probability 0.2. Event B occurs with probability 0.3. Event C occurs with probability 0.4. If A, B, and C are disjoint, then which of the following probabilities is (are) correct?

Accepted Answer

A) P(A or 
B)  = 0.5 
B) P(A or 
C)  = 0.6 
C) P(A or B or 
C)  = 0.9 
D) All of these choices are correct. 
A) P(A or 
B)  = 0.5 
B) P(A or 
C)  = 0.6 
C) P(A or B or 
C)  = 0.9 
D) All of these choices are correct.

Question 8

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 (age 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:
?
?
$$\begin{array} { | l | l | l | l | l | l | l | l | l | } 
\hline \text { Days } X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline \text { Probability } & 0.04 & 0.03 & 0.06 & 0.08 & 0.09 & 0.08 & 0.05 & ? \
\hline
\end{array}$$ This is a legitimate probability model. Therefore, what is the value of P(X = 7)?

Accepted Answer

A) 1/7 
B) 1/8 
C) 0.43 
D) 0.57 
A) 1/7 
B) 1/8 
C) 0.43 
D) 0.57

Question 9

Event A has probability 0.4. Event B has probability 0.5. Event C has probability 0.6. Which of the following statements about these events must be TRUE?

Accepted Answer

A) Events A, B, and C are disjoint. 
B) One event must have some outcomes in common with at least one other event. 
C) The probability that event C does not occur is 0.9. 
D) The sample space for these events is larger than typical. 
A) Events A, B, and C are disjoint. 
B) One event must have some outcomes in common with at least one other event. 
C) The probability that event C does not occur is 0.9. 
D) The sample space for these events is larger than typical.

Question 10

A probability can be called a risk when it applies to an undesirable outcome.

Accepted Answer

A) True 
 B)False

Question 11

If X is a continuous uniform random variable taking values between 0 and 100, what is the numerical value of the probability P(X = 10.333)?

Accepted Answer

The answer of If X is a continuous uniform random...

Question 12

Which of the following terms describes an event that is uncertain but has a regular distribution over many outcomes?

Accepted Answer

A) Random 
B) Predictable 
C) Deterministic 
D) Chaotic 
A) Random 
B) Predictable 
C) Deterministic 
D) Chaotic

Question 13

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 gives the probability distribution for X.
?
?
$$\begin{array} { | l | l | l | l | l | l | l | l | l | l | } 
\hline X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \
\hline P ( X ) & 0.513 & 0.357 & 0.109 & 0.019 & 0.002 & 0.000 & 0.000 & 0.000 & 0.000 \
\hline
\end{array}$$ What is the mean of this distribution?

Accepted Answer

A) 0.640 
B) 0.766 
C) 0.096 
D) None of these choices is correct. 
A) 0.640 
B) 0.766 
C) 0.096 
D) None of these choices is correct.

Question 14

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 gives the probability distribution for X.
?
?
$$\begin{array} { | l | l | l | l | l | l | l | l | l | l | } 
\hline X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \
\hline P ( X ) & 0.513 & 0.357 & 0.109 & 0.019 & 0.002 & 0.000 & 0.000 & 0.000 & 0.000 \
\hline
\end{array}$$ Which is the correct notation for representing the probability of getting at least 4 color-blind individuals in the sample?

Accepted Answer

A) P(X  4) 
C) P(X ?4) 
D) P(X ? 4) 
A) P(X  4) 
C) P(X ?4) 
D) P(X ? 4)

Question 15

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 (age 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:
?
?
$$\begin{array} { | l | l | l | l | l | l | l | l | l | } 
\hline \text { Days } X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline \text { Probability } & 0.04 & 0.03 & 0.06 & 0.08 & 0.09 & 0.08 & 0.05 & ? \
\hline
\end{array}$$ What does the event X < 5 mean?

Accepted Answer

A) The student watched TV no more than 5 days in the past week. 
B) The student watched TV at least 5 days in the past week. 
C) The probability that the student watched TV in the past week is smaller than 5. 
D) The student watched TV fewer than 5 days in the past week. 
A) The student watched TV no more than 5 days in the past week. 
B) The student watched TV at least 5 days in the past week. 
C) The probability that the student watched TV in the past week is smaller than 5. 
D) The student watched TV fewer than 5 days in the past week.

Question 16

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

Accepted Answer

A) 1/3 
B) 1/2 
C) 3/4 
D) 1 
A) 1/3 
B) 1/2 
C) 3/4 
D) 1

Question 17

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

Accepted Answer

A) The probability of any event is the area under the density curve over the range of values that make up the event. 
B) The total area under the density curve must be exactly 1. 
C) If X is a continuous random variable taking values between 0 and 500, then P(X > 200) = P(X ≥ 200). 
D) There are no disjoint events in continuous probability models. 
A) The probability of any event is the area under the density curve over the range of values that make up the event. 
B) The total area under the density curve must be exactly 1. 
C) If X is a continuous random variable taking values between 0 and 500, then P(X > 200) = P(X ≥ 200). 
D) There are no disjoint events in continuous probability models.

Question 18

A recent nationwide study of myopia (nearsightedness) found that 38.1% of Americans age 18 to 24 suffer from myopia. What is the risk of myopia in the 18- to 24-year-old American population?

Accepted Answer

A) 0.381 
B) 0.616 
C) 1.616 
D) 2.625 
A) 0.381 
B) 0.616 
C) 1.616 
D) 2.625

Question 19

All human blood can be typed as either 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:
?
?
$$\begin{array} { | l | l | l | l | l | } 
\hline \text { Blood type } & \text { O } & \text { A } & \text { B } & \text { AB } \
\hline \text { Probability } & 0.50 & ? & 0.20 & 0.05 \
\hline
\end{array}$$ Some people consider having type AB blood to be an undesirable outcome because it may be difficult to find matching donors. What is the risk of having type AB?

Accepted Answer

A) 0.05 
B) 0.95 
C) 1.05 
D) 20.0 
A) 0.05 
B) 0.95 
C) 1.05 
D) 20.0

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 (age 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:
?
?
$$\begin{array} { | l | l | l | l | l | l | l | l | l | } 
\hline \text { Days } X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline \text { Probability } & 0.04 & 0.03 & 0.06 & 0.08 & 0.09 & 0.08 & 0.05 & ? \
\hline
\end{array}$$ What is the probability that a randomly selected student did not watch TV 7 days in the past week?

Accepted Answer

A) 0.43 
B) 0.57 
C) 6/7 
D) 7/8 
A) 0.43 
B) 0.57 
C) 6/7 
D) 7/8

Event A has probability 0.4. Event B has probability 0.5. If A and B are disjoint, what is the probability that both events occur?

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 are the odds of a diagnosis being incorrect?

An odds is the ratio of the probability of an outcome over the probability of that outcome not occurring.

Based on a recent Gallup survey, we define the following probability model for the number X of daily cups of coffee consumed by Americans. X 0 1 2 3 4 or more Probability 0.36 0.26 0.19 0.09 ? What is the probability that an American consumes at most 1 cup of coffee daily?

Event A occurs with probability 0.2. Event B occurs with probability 0.3. Event C occurs with probability 0.4. If A, B, and C are disjoint, then which of the following probabilities is (are) correct?

Event A has probability 0.4. Event B has probability 0.5. Event C has probability 0.6. Which of the following statements about these events must be TRUE?

A probability can be called a risk when it applies to an undesirable outcome.

If X is a continuous uniform random variable taking values between 0 and 100, what is the numerical value of the probability P(X = 10.333)?

Which of the following terms describes an event that is uncertain but has a regular distribution over many outcomes?

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

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

A recent nationwide study of myopia (nearsightedness) found that 38.1% of Americans age 18 to 24 suffer from myopia. What is the risk of myopia in the 18- to 24-year-old American population?

Picturing Distributions With Graphs

Describing Quantitative Distributions With Numbers

Scatterplots and Correlation

Regression

Two-Way Tables

Samples and Observational Studies

Designing Experiments

Independence and Conditional Probabilities

The Normal Distributions

Discrete Probability Distributions

Sampling Distributions

Introduction to Inference

Exercises

Inference About a Population Mean

Comparing Two Means

Inference About a Population Proportion

Comparing Two Proportions

The Chi-Square Test for Goodness of Fit

The Chi-Square Test for Two-Way Tables

Inference for Regression

One-Way Analysis of Variance: Comparing Several Means

More About Analysis of Variance: Follow-Up Tests and Two-Way Anova

Nonparametric Tests

Multiple and Logistic Regression

Filters

Exam 8: Essential Probability Rules

Event A has probability 0.4. Event B has probability 0.5. If A and B are disjoint, what is the probability that both events occur?

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 are the odds of a diagnosis being incorrect?

An odds is the ratio of the probability of an outcome over the probability of that outcome not occurring.

Based on a recent Gallup survey, we define the following probability model for the number X of daily cups of coffee consumed by Americans. ​ ​ X 0 1 2 3 4 or more Probability 0.36 0.26 0.19 0.09 ? What is the probability that an American consumes at most 1 cup of coffee daily?

Event A occurs with probability 0.2. Event B occurs with probability 0.3. Event C occurs with probability 0.4. If A, B, and C are disjoint, then which of the following probabilities is (are) correct?

Event A has probability 0.4. Event B has probability 0.5. Event C has probability 0.6. Which of the following statements about these events must be TRUE?

A probability can be called a risk when it applies to an undesirable outcome.

If X is a continuous uniform random variable taking values between 0 and 100, what is the numerical value of the probability P(X = 10.333)?

Which of the following terms describes an event that is uncertain but has a regular distribution over many outcomes?

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

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

A recent nationwide study of myopia (nearsightedness) found that 38.1% of Americans age 18 to 24 suffer from myopia. What is the risk of myopia in the 18- to 24-year-old American population?

Picturing Distributions With Graphs

Describing Quantitative Distributions With Numbers

Scatterplots and Correlation

Regression

Two-Way Tables

Samples and Observational Studies

Designing Experiments

Independence and Conditional Probabilities

The Normal Distributions

Discrete Probability Distributions

Sampling Distributions

Introduction to Inference

Exercises

Inference About a Population Mean

Comparing Two Means

Inference About a Population Proportion

Comparing Two Proportions

The Chi-Square Test for Goodness of Fit

The Chi-Square Test for Two-Way Tables

Inference for Regression

One-Way Analysis of Variance: Comparing Several Means

More About Analysis of Variance: Follow-Up Tests and Two-Way Anova

Nonparametric Tests

Multiple and Logistic Regression

Filters

Based on a recent Gallup survey, we define the following probability model for the number X of daily cups of coffee consumed by Americans. X 0 1 2 3 4 or more Probability 0.36 0.26 0.19 0.09 ? What is the probability that an American consumes at most 1 cup of coffee daily?