Question 1

Determine whether the events A and B are independent.
-A person is selected at random from a group of college students. 
Event A: The person selected is a woman
Event B: The person selected votes Republican

Accepted Answer

A) True 
 B)False

Question 2

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-When a pair of dice is rolled there are 36 different possible outcomes: $1 - 1,1 - 2 , \ldots 6$ - If a pair of dice is rolled 4 times, what is the probability of getting a sum of 5 every time?

Accepted Answer

A)  $\frac { 625 } { 1,679,616 }$ 
B)  $\frac { 1 } { 1296 }$ 
C)  $\frac { 4 } { 9 }$ 
D)  $\frac { 1 } { 6561 }$

Question 3

Solve the problem.
-There are 6 women running in a race. How many different ways could first, second, and third place finishers occur?

Accepted Answer

A) 120 
B) 216 
C) 20 
D) 18

Question 4

Make a probability distribution for the given set of events.
-The following table displays a frequency distribution of the number of siblings for students at one middle school. Make a probability distribution for number of siblings. $\begin{array}{r|rrrrrrrr}
\text { Number of siblings } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline \text { Frequency } & 188 & 257 & 135 & 54 & 22 & 8 & 6 & 3
\end{array}$

Accepted Answer

A) 
$\begin{array}{r|r}
\text { Siblings } & \text { Probability } \
\hline 0 & 0.125 \
1 & 0.125 \
2 & 0.125 \
3 & 0.125 \
4 & 0.125 \
5 & 0.125 \
6 & 0.125 \
7 & 0.125
\end{array}$ 
B) 
$\begin{array}{r|r}
\text { Siblings } & \text { Probability } \
\hline 1 & 0.530 \
2 & 0.278 \
3 & 0.111 \
4 & 0.045 \
5 & 0.016 \
6 & 0.012 \
7 & 0.006
\end{array}$ 
C) 
$\begin{array}{r|r}
\text { Siblings } & \text { Probability } \
\hline 0 & 0.279 \
1 & 0.382 \
2 & 0.201 \
3 & 0.080 \
4 & 0.033 \
5 & 0.012 \
6 & 0.009 \
7 & 0.004
\end{array}$ 
D) 
$\begin{array}{r|r}
\text { Siblings } & \text { Probability } \
\hline 0 & 0.294 \
1 & 0.367 \
2 & 0.212 \
3 & 0.068 \
4 & 0.033 \
5 & 0.012 \
6 & 0.009 \
7 & 0.004
\end{array}$

Question 5

Use the at least once rule to find the indicated probability.
-The probability that a certain region in Mexico will be hit by a hurricane in any given year is 0.02. What is the probability that the region will be hit by at least one hurricane in the next 15 years?

Accepted Answer

A) 0.980 
B) 0.015 
C) 0.739 
D) 0.261

Question 6

Provide an appropriate response.
-Suppose that 4 items are to be selected from N items and that repetitions are not allowed. Which of the following is true?

Accepted Answer

A) There are 4 times as many permutations as combinations. 
B) There are 4 times as many combinations as permutations. 
C) There are 24 times as many combinations as permutations. 
D) There are 24 times as many permutations as combinations.

Question 7

Solve the problem.
-A local department store sells carpets in 4 sizes. Each carpet comes in 3 different qualities. One of the sizes comes in 5 colors. The other sizes come in 2 colors. How many choices of carpet are there?

Accepted Answer

A) 39 
B) 40 
C) 33 
D) 38

Question 8

Provide an appropriate response.
-When a balanced die is rolled, the probability that a four will appear is $\frac { 1 } { 6 }$ Which of the following statements is a reasonable conclusion? A: If I roll a balanced die 6 times I will get one four
B: If I roll a balanced die 300 times I will get fifty fours
C: If I roll a balanced die 1200 times, I will get approximately 200 fours

Accepted Answer

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

Question 9

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-A class consists of 11 women and 44 men. If a student is randomly selected, what is the probability that the student is a woman?

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 55 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $\frac { 4 } { 5 }$

Question 10

Use the at least once rule to find the indicated probability.
-In a batch of 8000 clock radios 3% are defective. A sample of 7 clock radios is randomly selected without replacement from the 8,000 and tested. The entire batch will be rejected if at least one of
Those tested is defective. What is the probability that the entire batch will be rejected?

Accepted Answer

A) 0.192 
B) 0.0300 
C) 0.143 
D) 0.808

Question 11

Find the expected value.
-Numbers is a game where you bet $1.00 on any three-digit number from 000 to 999. If your number comes up, you get $600.00. If your number doesn't come up, you lose your $1. Find the
Expected net winnings.

Accepted Answer

A) -$0.42 
B) -$0.50 
C) -$1.00 
D) -$0.40

Question 12

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-A fair die is rolled. What is the probability of rolling a 3 or a 4?

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B)  $\frac { 1 } { 36 }$ 
C)  2 
D)  $\frac { 1 } { 6 }$

Question 13

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-A family has five children. The probability of having a girl is 0.5. What is the probability of having 3 girls followed by 2 boys?

Accepted Answer

A)  $\frac { 5 } { 16 }$ 
B)  $\frac { 1 } { 32 }$ 
C)  $\frac { 1 } { 16 }$ 
D)  $\frac { 1 } { 120 }$

Question 14

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

Accepted Answer

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

Question 15

Provide an appropriate response.
-Chantal noted that there are two equally likely outcomes when you flip a fair coin and heads is one of those outcomes. She concluded that the probability of getting heads on a flip of a fair coin is 1/2 .
Which method did Chantal use?

Accepted Answer

A) Empirical method 
B) Relative frequency method 
C) Subjective method 
D) Theoretical method

Question 16

Solve the problem.
-A company wants to hire a software engineer, an administrative assistant, and a sales representative. There are 4 possible candidates for the position of software engineer, 4 for the
Position of administrative assistant, and 3 for the position of sales representative. How many ways
Are there to choose the three people who will be hired?

Accepted Answer

A) 48 
B) 64 
C) 11 
D) 24

Question 17

Given that $P ( E ) = 1$, what must be true about the event $E$ ?

Accepted Answer

A)  The event $E$ is certain. 
B)  The event $E$ is impossible. 
C)  The event $E$ is probable but not certain. 
D)  The event $E$ is possible but not likely.

Question 18

Determine whether the events A and B are independent.
-A card is selected at random from a standard deck of 52 cards. It is then replaced and a second card is selected at random.
Event A: A club is selected on the first draw
Event B: An ace is selected on the second draw

Accepted Answer

A) True 
 B)False

Question 19

Solve the problem.
-In a certain lottery, 6 different numbers between 1 and 8 inclusive are drawn. These are the winning numbers. How many different selections are possible? Assume that the order in which the
Numbers are drawn is unimportant.

Accepted Answer

A) 262,144 
B) 720 
C) 28 
D) 20,160

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. $$\begin{array} { l | r } 
{ \text { Cause of Death } } & \text { Deaths } \
\hline \text { Heart Disease } & 162,750 \
\text { Cancer } & 147,250 \
\text { AIDS } & 65,875 \
\text { Stroke } & 44,175 \
\text { Pulmonary Disease } & 43,555 \
\text { Accidents } & 41,850 \
\text { Diabetes } & 18,755 \
\text { Pneumonia } & 17,360 \
\text { Kidney Disease } & 9145
\end{array}$$ Assume a population of 77.5 million. In a typical city of 500,000, how many people would you expect to die of cancer in a year?

Accepted Answer

A) Approximately 73,625 people 
B) Approximately 9500 people 
C) Approximately 950 people 
D) Approximately 7363 people

Exam 7: Probability: Living With the Odds

Determine whether the events A and B are independent. -A person is selected at random from a group of college students. Event A: The person selected is a woman Event B: The person selected votes Republican

Find the indicated probability. Round your answer to 6 decimal places when necessary. -When a pair of dice is rolled there are 36 different possible outcomes: $1 - 1,1 - 2 , \ldots 6$ - If a pair of dice is rolled 4 times, what is the probability of getting a sum of 5 every time?

Solve the problem. -There are 6 women running in a race. How many different ways could first, second, and third place finishers occur?

Use the at least once rule to find the indicated probability. -The probability that a certain region in Mexico will be hit by a hurricane in any given year is 0.02. What is the probability that the region will be hit by at least one hurricane in the next 15 years?

Provide an appropriate response. -Suppose that 4 items are to be selected from N items and that repetitions are not allowed. Which of the following is true?

Solve the problem. -A local department store sells carpets in 4 sizes. Each carpet comes in 3 different qualities. One of the sizes comes in 5 colors. The other sizes come in 2 colors. How many choices of carpet are there?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A class consists of 11 women and 44 men. If a student is randomly selected, what is the probability that the student is a woman?

Find the expected value. -Numbers is a game where you bet $1.00 on any three-digit number from 000 to 999. If your number comes up, you get $600.00. If your number doesn't come up, you lose your $1. Find the Expected net winnings.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A fair die is rolled. What is the probability of rolling a 3 or a 4?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A family has five children. The probability of having a girl is 0.5. What is the probability of having 3 girls followed by 2 boys?

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

Provide an appropriate response. -Chantal noted that there are two equally likely outcomes when you flip a fair coin and heads is one of those outcomes. She concluded that the probability of getting heads on a flip of a fair coin is 1/2 . Which method did Chantal use?

Given that $P ( E ) = 1$ , what must be true about the event $E$ ?

Determine whether the events A and B are independent. -A card is selected at random from a standard deck of 52 cards. It is then replaced and a second card is selected at random. Event A: A club is selected on the first draw Event B: An ace is selected on the second draw

Solve the problem. -In a certain lottery, 6 different numbers between 1 and 8 inclusive are drawn. These are the winning numbers. How many different selections are possible? Assume that the order in which the Numbers are drawn is unimportant.