Question 1

Provide an appropriate response.
-Identify the sample space of the probability experiment: recording the number of days it snowed in Cleveland
in the month of January.

Accepted Answer

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-Identify the sample space...

Question 2

Provide an appropriate response.
-Identify the sample space of the probability experiment: answering a multiple choice question with A, B, C, and
D as the possible answers

Accepted Answer

The answer of Provide an appropriate response.
-Identify the sample space...

Question 3

Provide an appropriate response.
-Identify the sample space of the probability experiment: answering a true or false question

Accepted Answer

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-Identify the sample space...

Question 4

Determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your
reasoning.
-You randomly select one card from a standard deck. Event B is selecting the ace of hearts.

Accepted Answer

The event of selecting the ace of hearts from a standard deck of cards has only one outcome, making it a simple event.

Question 5

Provide an appropriate response.
-Classify the statement as an example of classical probability, empirical probability, or subjective probability. The probability that interest rates will rise during the summer is 0.05.

Accepted Answer

This is an example of subjective probability because it is based on personal judgment or opinion rather than on exact calculations or specific past events.

Question 6

Provide an appropriate response.
-Identify the sample space of the probability experiment: recording a response to the survey question and the
gender of the respondent. $\text {Americans say keep the penny }$
$\text {Do you favor abolishing the penny?}$

$\text {Source: Harris interactive poll of 2136 adults taken June 10-16. }$
$\text {By Shannon Reilly and Robert W. Ahrens, USA. Today}$

Accepted Answer

The answer of Provide an appropriate response.
-Identify the sample space...

Question 7

Use the fundamental counting principle to solve the problem.
-If 12 newborn babies are randomly selected, how many different gender sequences are possible?

Accepted Answer

For each baby, there are 2 possibilities (male or female). Therefore, for 12 babies, there are $2^{12} = 4096$ different gender sequences possible.

Question 8

Provide an appropriate response.
-Identify the sample space of the probability experiment: recording the day of the week and whether or not it
rains.

Accepted Answer

The answer of Provide an appropriate response.
-Identify the sample space...

Question 9

Provide an appropriate response.
-Identify the sample space of the probability experiment: A calculator has a function button to generate a
random integer from -5 to 5

Accepted Answer

The answer of Provide an appropriate response.
-Identify the sample space...

Question 10

Use the fundamental counting principle to solve the problem.
-How many license plates can be made consisting of 3 letters followed by 2 digits?

Accepted Answer

There are 26 choices for each of the 3 letters (26x26x26) and 10 choices for each of the 2 digits (10x10). Using the fundamental counting principle, we multiply the number of choices for each set of characters: (26x26x26)(10x10) = 1,757,600. Therefore, the answer is A) 1,757,600. There are 26 letters in the alphabet, so there are 26 choices for the first letter, 26 choices for the second letter, and 26 choices for the third letter. There are 10 digits (0-9), so there are 10 choices for the fourth digit and 10 choices for the fifth digit. Therefore, by the fundamental counting principle, the total number of license plates that can be made is 26 x 26 x 26 x 10 x 10 = 1,757,600.

Question 11

Determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your
reasoning.
-A computer is used to randomly select a number between 1 and 1000. Event A is selecting a number greater than 600.

Accepted Answer

Event A is selecting a number greater than 600, which means there are 400 possible outcomes (from 601 to 1000). It is not a simple event because it consists of multiple outcomes. Event A is not a simple event because it consists of more than one outcome. There are 400 possible outcomes because any number greater than 600 but less than or equal to 1000 is a possible outcome.

Question 12

Determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your
reasoning.
-You randomly select a computer from a batch of 50 which contains 3 defective computers. Event B is selecting a defective computer.

Accepted Answer

Event B, selecting a defective computer, has 3 outcomes because there are 3 defective computers in the batch. It is not a simple event because it consists of more than one outcome (selecting any one of the 3 defective computers).

Question 13

Determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your
reasoning.
-You roll a six-sided die. Event B is rolling an even number.

Accepted Answer

The event of rolling an even number on a six-sided die includes rolling a 2, 4, or 6, which are three outcomes. It is not a simple event because it consists of more than one outcome.

Question 14

Use the fundamental counting principle to solve the problem.
-How many different codes of 4 digits are possible if the first digit must be 3, 4, or 5 and if the code may not end in 0?

Accepted Answer

For the first digit, there are 3 choices (3, 4, or 5). For each of the next two digits, there are 10 choices (0 through 9). For the last digit, there are 9 choices (1 through 9, since it cannot be 0). Thus, the total number of codes is 3 * 10 * 10 * 9 = 2700.

Question 15

Provide an appropriate response.
-Identify the sample space of the probability experiment: rolling a pair of 12-sided dice (with sides numbered
1-12)and observing the total number of points of each roll

Accepted Answer

The answer of Provide an appropriate response.
-Identify the sample space...

Question 16

Use the fundamental counting principle to solve the problem.
-A shirt company has 4 designs each of which can be made with short or long sleeves. There are 5 color patterns available. How many different shirts are available from this company?

Accepted Answer

By using the fundamental counting principle, we can find the total number of different shirts by multiplying the number of choices for each category. In this case, there are 4 choices for sleeve length and 5 choices for color pattern. Therefore, the total number of different shirts is 4 x 5 = 20. To use the fundamental counting principle, we multiply the number of choices for each category. In this case, there are 4 designs and each design can be made with 2 sleeve lengths, giving us 4 x 2 = 8 options. Multiplying this by the 5 color patterns available, we get 8 x 5 = 40 different shirts available. Therefore, the answer is A).

Question 17

Provide an appropriate response.
-Classify the statement as an example of classical probability, empirical probability, or subjective probability. The probability that a train will be in an accident on a specific route is 1%.

Accepted Answer

Empirical probability is based on observed data, and the statement suggests that the probability is derived from historical data on train accidents on that specific route.

Question 18

Provide an appropriate response.
-Identify the sample space of the probability experiment: rolling a single 12-sided die with sides numbered 1-12

Accepted Answer

The answer of Provide an appropriate response.
-Identify the sample space...

Question 19

Provide an appropriate response.
-Identify the sample space of the probability experiment: determining the childrenʹs gender for a family of three
children (Use B for boy and G for girl.)

Accepted Answer

The answer of Provide an appropriate response.
-Identify the sample space...

Question 20

Use the fundamental counting principle to solve the problem.
-A singer-songwriter wishes to compose a melody. Each note in the melody must be one of the 12 notes in her vocal range. How many different sequences of 3 notes are possible?

Accepted Answer

For each note in the 3-note sequence, there are 12 possible choices, making the total number of different sequences 12 * 12 * 12 = 1728.

Quiz 3: Probability

Provide an appropriate response. -Identify the sample space of the probability experiment: recording the number of days it snowed in Cleveland in the month of January.

Provide an appropriate response. -Identify the sample space of the probability experiment: answering a multiple choice question with A, B, C, and D as the possible answers

Provide an appropriate response. -Identify the sample space of the probability experiment: answering a true or false question

Determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning. -You randomly select one card from a standard deck. Event B is selecting the ace of hearts.

Provide an appropriate response. -Classify the statement as an example of classical probability, empirical probability, or subjective probability. The probability that interest rates will rise during the summer is 0.05.

Use the fundamental counting principle to solve the problem. -If 12 newborn babies are randomly selected, how many different gender sequences are possible?

Provide an appropriate response. -Identify the sample space of the probability experiment: recording the day of the week and whether or not it rains.

Provide an appropriate response. -Identify the sample space of the probability experiment: A calculator has a function button to generate a random integer from -5 to 5

Use the fundamental counting principle to solve the problem. -How many license plates can be made consisting of 3 letters followed by 2 digits?

Determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning. -A computer is used to randomly select a number between 1 and 1000. Event A is selecting a number greater than 600.

Determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning. -You randomly select a computer from a batch of 50 which contains 3 defective computers. Event B is selecting a defective computer.

Determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning. -You roll a six-sided die. Event B is rolling an even number.

Use the fundamental counting principle to solve the problem. -How many different codes of 4 digits are possible if the first digit must be 3, 4, or 5 and if the code may not end in 0?

Provide an appropriate response. -Identify the sample space of the probability experiment: rolling a pair of 12-sided dice (with sides numbered 1-12)and observing the total number of points of each roll

Use the fundamental counting principle to solve the problem. -A shirt company has 4 designs each of which can be made with short or long sleeves. There are 5 color patterns available. How many different shirts are available from this company?

Provide an appropriate response. -Classify the statement as an example of classical probability, empirical probability, or subjective probability. The probability that a train will be in an accident on a specific route is 1%.

Provide an appropriate response. -Identify the sample space of the probability experiment: rolling a single 12-sided die with sides numbered 1-12

Provide an appropriate response. -Identify the sample space of the probability experiment: determining the childrenʹs gender for a family of three children (Use B for boy and G for girl.)

Use the fundamental counting principle to solve the problem. -A singer-songwriter wishes to compose a melody. Each note in the melody must be one of the 12 notes in her vocal range. How many different sequences of 3 notes are possible?