Question 1

Decide whether events A and B are overlapping or non-overlapping.
-A student is selected at random. Event A is that the student speaks Spanish and event B is that the student speaks Chinese.

Accepted Answer

A) Non-overlapping 
B) Overlapping

Question 2

Solve the problem. Round your answer to 2 decimal places when necessary.
-In a given year, the population of a certain country is about 224 million. The overall birth rate is 18.2 births per 1000. The overall death rate is 10.1 deaths per 1000. Based on births and deaths
Alone (not counting immigration), about how much does the population of the country increase
During this year?

Accepted Answer

A) 4.08 million people 
B) 18.14 million people 
C) 0.18 million people 
D) 1.81 million people

Question 3

Solve the problem. Round your answer to 5 decimal places when necessary.
-The table shows the leading causes of death for one country in a single recent year. $$\begin{array} { l | r } 
 { \text { Cause of Death } } & \text { Deaths } \
\hline \text { Heart Disease } & 192,150 \
\text { Cancer } & 146,400 \
\text { AIDS } & 75,030 \
\text { Stroke } & 54,900 \
\text { Pulmonary Disease } & 51,423 \
\text { Accidents } & 48,495 \
\text { Diabetes } & 22,143 \
\text { Pneumonia } & 20,496 \
\text { Kidney Disease } & 10,797
\end{array}$$ Assume a population of 91.5 million. In a typical city of 500,000 , how many people would you expect to die by accident in a year?

Accepted Answer

A) Approximately 24,247.5 people 
B) Approximately 2425 people 
C) Approximately 2650 people 
D) Approximately 265 people

Question 4

Solve the problem.
-A shirt company has 4 designs each of which can be made with short or long sleeves. There are 6 different colors available. How many different shirts are available from this company?

Accepted Answer

A) 48 
B) 10 
C) 24 
D) 12

Question 5

Solve the problem. Round your answer to 5 decimal places when necessary.
-The table shows the leading causes of death for one country in a single recent year. $$\begin{array} { l | r } 
{ \text { Cause of Death } } & \text { Deaths } \
\hline \text { Heart Disease } & 205,850 \
\text { Cancer } & 143,200 \
\text { AIDS } & 85,025 \
\text { Stroke } & 55,490 \
\text { Pulmonary Disease } & 50,299 \
\text { Accidents } & 41,170 \
\text { Diabetes } & 21,659 \
\text { Pneumonia } & 20,048 \
\text { Kidney Disease } & 10,561
\end{array}$$ Assume a population of 89.5 million. What is the death rate due to heart disease in deaths per 100,000 of the population?

Accepted Answer

A) 23 deaths per 100,000 
B) 2.0585 deaths per 100,000 
C) 230 deaths per 100,000 
D) 20.585 deaths per 100,000

Question 6

Write the word or phrase that best completes each statement or answers the question.
-A game is said to be "fair" if the expected value for winnings is 0, that is, in the long run,
the player can expect to win 0. Consider the following game. The game costs $1 to play and
the payoffs are $5 for red, $3 for blue, $2 for yellow, and nothing for white. The following
probabilities apply. What are your expected winnings? Does the game favor the player or
the owner? $$\begin{array} { r | r } 
\text { Outcome } & \text { Probability } \
\hline \text { Red } & .02 \
\text { Blue } & .04 \
\text { Yellow } & .16 \
\text { White } & .78
\end{array}$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 7

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-Find the probability of tossing 5 tails, then 5 heads, on the first 10 tosses of a fair coin.

Accepted Answer

A) 0.000977 
B) 0.03125 
C) 0.001953 
D) 5

Question 8

Provide an appropriate response.
-Which of the following events has a probability of 1? A: I will get a perfect score on my math test if I study
B: I will die some day
C: The world will go on turning if I fail my test

Accepted Answer

A) A and B 
B) All of them 
C) B only 
D) B and C 
E) A and C

Question 9

Decide whether events A and B are overlapping or non-overlapping.
-You roll a red die and a blue die. Event A is that you get a sum of 11.
Event B is that you get a one on the blue die.

Accepted Answer

A) Overlapping 
B) Non-overlapping

Question 10

Solve the problem.
-Ten thousand raffle tickets are sold. One first prize of $1600, 5 second prizes of $1000 each, and 10 third prizes of $200 each are to be awarded, with all winners selected randomly. If you are given
One ticket, what are your expected winnings?

Accepted Answer

A) 126 cents 
B) 86 cents 
C) 28 cents 
D) 150 cents

Question 11

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-Find the probability of correctly answering the first 3 questions on a multiple choice test if random guesses are made and each question has 4 possible answers.

Accepted Answer

A)  $\frac { 3 } { 4 }$ 
B)  $\frac { 1 } { 81 }$ 
C)  $\frac { 4 } { 3 }$ 
D)  $\frac { 1 } { 64 }$

Question 12

Solve the problem.
-Four married couples have reserved eight seats in a row at the theater. If they arrange themselves randomly, what is the probability that all the women will sit in adjacent seats and all the men will
Sit in adjacent seats?

Accepted Answer

A)  $\frac { 1 } { 840 }$ 
B)  $\frac { 1 } { 35 }$ 
C)  $\frac { 1 } { 70 }$ 
D)  $\frac { 2 } { 315 }$

Question 13

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-If you are dealt two cards successively (with replacement of the first)from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second.

Accepted Answer

A)  $\frac { 13 } { 204 }$ 
B)  $\frac { 1 } { 169 }$ 
C)  $\frac { 1 } { 16 }$ 
D)  $\frac { 1 } { 204 }$

Question 14

Find the expected value.
-A bus arrives at a bus stop at 10 am, 10 minutes past ten, and 11.00 am. You arrive at the bus stop at random times between 10.00 am and 11.00 am every day, so all arrival times are equally likely.
Find your expected waiting time for the bus.
[Hint: Find the probability that you will arrive at the bus stop between 10.00 am and 10 minutes
Past ten and find your mean waiting time in that case. Then find the probability that you will arrive
At the bus stop between 10 minutes past ten and 11.00 am and find your mean waiting time in that
Case.]

Accepted Answer

A) 21.7 minutes 
B) 15 minutes 
C) 22.5 minutes 
D) 43.3 minutes

Question 15

Provide an appropriate response.
-When using the counting rules to count the number of possible outcomes, the permutation formula can be used in which of the following situations?

Accepted Answer

A) When repetitions are allowed and the order of arrangement is important 
B) When repetitions are allowed and the order of arrangement is unimportant 
C) When repetitions are not allowed and the order of arrangement is important 
D) When repetitions are not allowed and the order of arrangement is unimportant

Question 16

Solve the problem.
-If it has been determined that the probability of an earthquake occurring on a certain day in a certain area is 0.05, what are the odds against an earthquake?

Accepted Answer

A) 1 to 20 
B) 19 to 1 
C) 18 to 1 
D) 20 to 1

Question 17

Solve the problem.
-The library is to be given 5 books as a gift. The books will be selected from a list of 21 titles. If each book selected must have a different title, how many possible selections are there?

Accepted Answer

A) 194,481 
B) 4,084,101 
C) 20,349 
D) 2,441,880

Question 18

Solve the problem.
-Suppose you are playing a game of chance. If you bet $7 on a certain event, you will collect $252 (including your $7 bet)if you win. Find the odds used for determining the payoff.

Accepted Answer

A)  $36 : 1$ 
B)  $1 : 35$ 
C)  $35 : 1$ 
D)  $252 : 259$

Question 19

Solve the problem.
-A pollster wants to minimize the effect the order of the questions has on a person's response to a survey. How many different surveys are required to cover all possible arrangements if there are 6
Questions on the survey?

Accepted Answer

A) 120 
B) 6 
C) 720 
D) 36

Question 20

Solve the problem. Round your answer to 5 decimal places when necessary.
-The table shows the leading causes of death for one country in a single recent year.  Assume a population of 86.5 million. How much greater is the risk of death by heart disease than the risk of death by stroke?

Accepted Answer

A) 4.13793 
B) 3.72414 
C) 41.37931 
D) 0.00182

Exam 7: Probability: Living With the Odds

Decide whether events A and B are overlapping or non-overlapping. -A student is selected at random. Event A is that the student speaks Spanish and event B is that the student speaks Chinese.

Solve the problem. -A shirt company has 4 designs each of which can be made with short or long sleeves. There are 6 different colors available. How many different shirts are available from this company?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Find the probability of tossing 5 tails, then 5 heads, on the first 10 tosses of a fair coin.

Provide an appropriate response. -Which of the following events has a probability of 1? A: I will get a perfect score on my math test if I study B: I will die some day C: The world will go on turning if I fail my test

Decide whether events A and B are overlapping or non-overlapping. -You roll a red die and a blue die. Event A is that you get a sum of 11. Event B is that you get a one on the blue die.

Solve the problem. -Ten thousand raffle tickets are sold. One first prize of $1600, 5 second prizes of $1000 each, and 10 third prizes of $200 each are to be awarded, with all winners selected randomly. If you are given One ticket, what are your expected winnings?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Find the probability of correctly answering the first 3 questions on a multiple choice test if random guesses are made and each question has 4 possible answers.

Solve the problem. -Four married couples have reserved eight seats in a row at the theater. If they arrange themselves randomly, what is the probability that all the women will sit in adjacent seats and all the men will Sit in adjacent seats?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -If you are dealt two cards successively (with replacement of the first) from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second.

Provide an appropriate response. -When using the counting rules to count the number of possible outcomes, the permutation formula can be used in which of the following situations?

Solve the problem. -If it has been determined that the probability of an earthquake occurring on a certain day in a certain area is 0.05, what are the odds against an earthquake?

Solve the problem. -The library is to be given 5 books as a gift. The books will be selected from a list of 21 titles. If each book selected must have a different title, how many possible selections are there?

Solve the problem. -Suppose you are playing a game of chance. If you bet $7 on a certain event, you will collect $252 (including your $7 bet) if you win. Find the odds used for determining the payoff.

Solve the problem. -A pollster wants to minimize the effect the order of the questions has on a person's response to a survey. How many different surveys are required to cover all possible arrangements if there are 6 Questions on the survey?

Solve the problem. Round your answer to 5 decimal places when necessary. -The table shows the leading causes of death for one country in a single recent year. Assume a population of 86.5 million. How much greater is the risk of death by heart disease than the risk of death by stroke?