# Common Core: High School - Statistics and Probability : Two-Way Frequency Tables: CCSS.Math.Content.HSS-CP.A.4

## Example Questions

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### Example Question #1 : Two Way Frequency Tables: Ccss.Math.Content.Hss Cp.A.4

A high school wants to assess the science elective courses that its students have chosen for their next year of education. Thirty-three freshmen, ten sophomores, eight juniors, and twenty-two seniors chose to take astronomy. Eighteen freshmen, twenty-four sophomores, thirty-three juniors, and twenty seniors are planning to take ecology. Twelve freshmen, thirty-eight sophomores, eighteen juniors, and twenty-five seniors want to take physics. Last, four freshmen, fourteen sophomores, fifteen juniors, and twenty-eight seniors chose to take chemistry.

Use this information to create a two-way frequency table and calculate the probability that a senior will take astronomy.

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

In order to solve this problem, we need to discuss probabilities and frequency charts. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

Let's use a simple example: the rolling of a die. We want to know the probability of rolling a one. We know that the sample space is six because there are six sides or outcomes to the die. Also, we know that there is only a single side with a value of one; therefore,

Now, let's convert this into a percentage:

Probabilities expressed in fraction form will have values between zero and one. One indicates that an event will definitely occur, while zero indicates that an event will not occur. Likewise, probabilities expressed as percentages possess values between zero and one hundred percent where probabilities closer to zero are unlikely to occur and those close to one hundred percent are more likely to occur.

Now, we will start by constructing a table. The question presents data associated with two different types of variables: grade level and class. There are four grade levels (i.e. freshman, sophomores, juniors, and seniors) and four elective science classes (i.e. astronomy, ecology, physics, and chemistry). We need to make a table that has four rows and four columns. Next, we can input the data contained in the table. Last we will add up each row and column in order to gain totals for each variable. If you have done this properly, then you should have created a table similar to the following:

After, the two-way table has been constructed you can then use it to solve the question: what is the probability that a senior will take astronomy?

First, we need to create the following ratio: number seniors planning to take the astrology class to the total number of seniors.

Substitute values using the table and solve.

### Example Question #2 : Two Way Frequency Tables: Ccss.Math.Content.Hss Cp.A.4

A high school wants to assess the science elective courses that its students have chosen for their next year of education. Thirty-three freshmen, ten sophomores, eight juniors, and twenty-two seniors chose to take astronomy. Eighteen freshmen, twenty-four sophomores, thirty-three juniors, and twenty seniors are planning to take ecology. Twelve freshmen, thirty-eight sophomores, eighteen juniors, and twenty-five seniors want to take physics. Last, four freshmen, fourteen sophomores, fifteen juniors, and twenty-eight seniors chose to take chemistry.

Use this information to create a two-way frequency table and calculate the probability that a senior will take astronomy.

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

Let's use a simple example: the rolling of a die. We want to know the probability of rolling a one. We know that the sample space is six because there are six sides or outcomes to the die. Also, we know that there is only a single side with a value of one; therefore,

Now, let's convert this into a percentage:

Probabilities expressed in fraction form will have values between zero and one. One indicates that an event will definitely occur, while zero indicates that an event will not occur. Likewise, probabilities expressed as percentages possess values between zero and one hundred percent where probabilities closer to zero are unlikely to occur and those close to one hundred percent are more likely to occur.

Now, we will start by constructing a table. The question presents data associated with two different types of variables: grade level and class. There are four grade levels (i.e. freshman, sophomores, juniors, and seniors) and four elective science classes (i.e. astronomy, ecology, physics, and chemistry). We need to make a table that has four rows and four columns. Next, we can input the data contained in the table. Last we will add up each row and column in order to gain totals for each variable. If you have done this properly, then you should have created a table similar to the following:

After, the two-way table has been constructed you can then use it to solve the question: what is the probability that a senior will take astronomy?

First we need to create the following ratio: number seniors planning to take the astrology class to the total number of seniors.

Substitute values using the table and solve.

### Example Question #3 : Two Way Frequency Tables: Ccss.Math.Content.Hss Cp.A.4

A high school wants to assess the science elective courses that its students have chosen for their next year of education. Six freshmen, thirty-three sophomores, eight juniors, and twenty-eight seniors chose to take astronomy. Eighteen freshmen, twenty-four sophomores, thirty-three juniors, and twenty seniors are planning to take ecology. Twelve freshmen, thirty-eight sophomores, eighteen juniors, and twenty-five seniors want to take physics. Last, four freshmen, fourteen sophomores, fifteen juniors, and twenty-eight seniors chose to take chemistry.

Use this information to create a two-way frequency table and calculate the probability that a senior will take astronomy.

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

Let's use a simple example: the rolling of a die. We want to know the probability of rolling a one. We know that the sample space is six because there are six sides or outcomes to the die. Also, we know that there is only a single side with a value of one; therefore,

Now, let's convert this into a percentage:

Probabilities expressed in fraction form will have values between zero and one. One indicates that an event will definitely occur, while zero indicates that an event will not occur. Likewise, probabilities expressed as percentages possess values between zero and one hundred percent where probabilities closer to zero are unlikely to occur and those close to one hundred percent are more likely to occur.

Now, we will start by constructing a table. The question presents data associated with two different types of variables: grade level and class. There are four grade levels (i.e. freshman, sophomores, juniors, and seniors) and four elective science classes (i.e. astronomy, ecology, physics, and chemistry). We need to make a table that has four rows and four columns. Next, we can input the data contained in the table. Last we will add up each row and column in order to gain totals for each variable. If you have done this properly, then you should have created a table similar to the following:

After, the two-way table has been constructed you can then use it to solve the question: what is the probability that a senior will take astronomy?

First, we need to create the following ratio: number seniors planning to take the astrology class to the total number of seniors.

Substitute values using the table and solve.

### Example Question #4 : Two Way Frequency Tables: Ccss.Math.Content.Hss Cp.A.4

A high school wants to assess the science elective courses that its students have chosen for their next year of education. Six freshmen, forty-nine sophomores, five juniors, and eighteen seniors chose to take astronomy. Eighteen freshmen, twenty-four sophomores, thirty-three juniors, and twenty seniors are planning to take ecology. Twelve freshmen, thirty-eight sophomores, eighteen juniors, and twenty-five seniors want to take physics. Last, four freshmen, fourteen sophomores, fifteen juniors, and twenty-eight seniors chose to take chemistry.

Use this information to create a two-way frequency table and calculate the probability that a senior will take astronomy.

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

Let's use a simple example: the rolling of a die. We want to know the probability of rolling a one. We know that the sample space is six because there are six sides or outcomes to the die. Also, we know that there is only a single side with a value of one; therefore,

Now, let's convert this into a percentage:

Probabilities expressed in fraction form will have values between zero and one. One indicates that an event will definitely occur, while zero indicates that an event will not occur. Likewise, probabilities expressed as percentages possess values between zero and one hundred percent where probabilities closer to zero are unlikely to occur and those close to one hundred percent are more likely to occur.

Now, we will start by constructing a table. The question presents data associated with two different types of variables: grade level and class. There are four grade levels (i.e. freshman, sophomores, juniors, and seniors) and four elective science classes (i.e. astronomy, ecology, physics, and chemistry). We need to make a table that has four rows and four columns. Next, we can input the data contained in the table. Last we will add up each row and column in order to gain totals for each variable. If you have done this properly, then you should have created a table similar to the following:

After, the two-way table has been constructed you can then use it to solve the question: what is the probability that a senior will take astronomy?

First, we need to create the following ratio: number seniors planning to take the astrology class to the total number of seniors.

Substitute values using the table and solve.

### Example Question #5 : Two Way Frequency Tables: Ccss.Math.Content.Hss Cp.A.4

A high school wants to assess the science elective courses that its students have chosen for their next year of education. Six freshmen, twelve sophomores, seven juniors, and thirty-seven seniors chose to take astronomy. Eighteen freshmen, twenty-four sophomores, thirty-three juniors, and twenty seniors are planning to take ecology. Twelve freshmen, thirty-eight sophomores, eighteen juniors, and twenty-five seniors want to take physics. Last, four freshmen, fourteen sophomores, fifteen juniors, and twenty-eight seniors chose to take chemistry.

Use this information to create a two-way frequency table and calculate the probability that a senior will take astronomy.

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

Let's use a simple example: the rolling of a die. We want to know the probability of rolling a one. We know that the sample space is six because there are six sides or outcomes to the die. Also, we know that there is only a single side with a value of one; therefore,

Now, let's convert this into a percentage:

Probabilities expressed in fraction form will have values between zero and one. One indicates that an event will definitely occur, while zero indicates that an event will not occur. Likewise, probabilities expressed as percentages possess values between zero and one hundred percent where probabilities closer to zero are unlikely to occur and those close to one hundred percent are more likely to occur.

Now, we will start by constructing a table. The question presents data associated with two different types of variables: grade level and class. There are four grade levels (i.e. freshman, sophomores, juniors, and seniors) and four elective science classes (i.e. astronomy, ecology, physics, and chemistry). We need to make a table that has four rows and four columns. Next, we can input the data contained in the table. Last we will add up each row and column in order to gain totals for each variable. If you have done this properly, then you should have created a table similar to the following:

After, the two-way table has been constructed you can then use it to solve the question: what is the probability that a senior will take astronomy?

First, we need to create the following ratio: number seniors planning to take the astrology class to the total number of seniors.

Substitute values using the table and solve.

### Example Question #6 : Two Way Frequency Tables: Ccss.Math.Content.Hss Cp.A.4

A high school wants to assess the science elective courses that its students have chosen for their next year of education. Six freshmen, twenty-eight sophomores, six juniors, and thirty-three seniors chose to take astronomy. Eighteen freshmen, twenty-four sophomores, thirty-three juniors, and twenty seniors are planning to take ecology. Twelve freshmen, thirty-eight sophomores, eighteen juniors, and twenty-five seniors want to take physics. Last, four freshmen, fourteen sophomores, fifteen juniors, and twenty-eight seniors chose to take chemistry.

Use this information to create a two-way frequency table and calculate the probability that a senior will take astronomy.

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

Let's use a simple example: the rolling of a die. We want to know the probability of rolling a one. We know that the sample space is six because there are six sides or outcomes to the die. Also, we know that there is only a single side with a value of one; therefore,

Now, let's convert this into a percentage:

Probabilities expressed in fraction form will have values between zero and one. One indicates that an event will definitely occur, while zero indicates that an event will not occur. Likewise, probabilities expressed as percentages possess values between zero and one hundred percent where probabilities closer to zero are unlikely to occur and those close to one hundred percent are more likely to occur.

Now, we will start by constructing a table. The question presents data associated with two different types of variables: grade level and class. There are four grade levels (i.e. freshman, sophomores, juniors, and seniors) and four elective science classes (i.e. astronomy, ecology, physics, and chemistry). We need to make a table that has four rows and four columns. Next, we can input the data contained in the table. Last we will add up each row and column in order to gain totals for each variable. If you have done this properly, then you should have created a table similar to the following:

After, the two-way table has been constructed you can then use it to solve the question: what is the probability that a senior will take astronomy?

First, we need to create the following ratio: number seniors planning to take the astrology class to the total number of seniors.

Substitute values using the table and solve.

### Example Question #7 : Two Way Frequency Tables: Ccss.Math.Content.Hss Cp.A.4

A high school wants to assess the science elective courses that its students have chosen for their next year of education. Eight freshmen, twenty-nine sophomores, seven juniors, and twenty-seven seniors chose to take astronomy. Eighteen freshmen, twenty-four sophomores, thirty-three juniors, and twenty seniors are planning to take ecology. Twelve freshmen, thirty-eight sophomores, eighteen juniors, and twenty-five seniors want to take physics. Last, four freshmen, fourteen sophomores, fifteen juniors, and twenty-eight seniors chose to take chemistry.

Use this information to create a two-way frequency table and calculate the probability that a senior will take astronomy.

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

Let's use a simple example: the rolling of a die. We want to know the probability of rolling a one. We know that the sample space is six because there are six sides or outcomes to the die. Also, we know that there is only a single side with a value of one; therefore,

Now, let's convert this into a percentage:

Probabilities expressed in fraction form will have values between zero and one. One indicates that an event will definitely occur, while zero indicates that an event will not occur. Likewise, probabilities expressed as percentages possess values between zero and one hundred percent where probabilities closer to zero are unlikely to occur and those close to one hundred percent are more likely to occur.

Now, we will start by constructing a table. The question presents data associated with two different types of variables: grade level and class. There are four grade levels (i.e. freshman, sophomores, juniors, and seniors) and four elective science classes (i.e. astronomy, ecology, physics, and chemistry). We need to make a table that has four rows and four columns. Next, we can input the data contained in the table. Last we will add up each row and column in order to gain totals for each variable. If you have done this properly, then you should have created a table similar to the following:

After, the two-way table has been constructed you can then use it to solve the question: what is the probability that a senior will take astronomy?

First, we need to create the following ratio: number seniors planning to take the astrology class to the total number of seniors.

Substitute values using the table and solve.

### Example Question #7 : Two Way Frequency Tables: Ccss.Math.Content.Hss Cp.A.4

A high school wants to assess the science elective courses that its students have chosen for their next year of education. Nine freshmen, twelve sophomores, seven juniors, and forty-four seniors chose to take astronomy. Eighteen freshmen, twenty-four sophomores, thirty-three juniors, and twenty seniors are planning to take ecology. Twelve freshmen, thirty-eight sophomores, eighteen juniors, and twenty-five seniors want to take physics. Last, four freshmen, fourteen sophomores, fifteen juniors, and twenty-eight seniors chose to take chemistry.

Use this information to create a two-way frequency table and calculate the probability that a senior will take astronomy.

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

Let's use a simple example: the rolling of a die. We want to know the probability of rolling a one. We know that the sample space is six because there are six sides or outcomes to the die. Also, we know that there is only a single side with a value of one; therefore,

Now, let's convert this into a percentage:

Probabilities expressed in fraction form will have values between zero and one. One indicates that an event will definitely occur, while zero indicates that an event will not occur. Likewise, probabilities expressed as percentages possess values between zero and one hundred percent where probabilities closer to zero are unlikely to occur and those close to one hundred percent are more likely to occur.

Now, we will start by constructing a table. The question presents data associated with two different types of variables: grade level and class. There are four grade levels (i.e. freshman, sophomores, juniors, and seniors) and four elective science classes (i.e. astronomy, ecology, physics, and chemistry). We need to make a table that has four rows and four columns. Next, we can input the data contained in the table. Last we will add up each row and column in order to gain totals for each variable. If you have done this properly, then you should have created a table similar to the following:

After, the two-way table has been constructed you can then use it to solve the question: what is the probability that a senior will take astronomy?

First, we need to create the following ratio: number seniors planning to take the astrology class to the total number of seniors.

Substitute values using the table and solve.

### Example Question #8 : Two Way Frequency Tables: Ccss.Math.Content.Hss Cp.A.4

A high school wants to assess the science elective courses that its students have chosen for their next year of education. Six freshmen, fifty-four sophomores, eight juniors, and forty-seven seniors chose to take astronomy. Eighteen freshmen, twenty-four sophomores, thirty-three juniors, and twenty seniors are planning to take ecology. Twelve freshmen, thirty-eight sophomores, eighteen juniors, and twenty-five seniors want to take physics. Last, four freshmen, fourteen sophomores, fifteen juniors, and twenty-eight seniors chose to take chemistry.

Use this information to create a two-way frequency table and calculate the probability that a senior will take astronomy.

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

Let's use a simple example: the rolling of a die. We want to know the probability of rolling a one. We know that the sample space is six because there are six sides or outcomes to the die. Also, we know that there is only a single side with a value of one; therefore,

Now, let's convert this into a percentage:

Probabilities expressed in fraction form will have values between zero and one. One indicates that an event will definitely occur, while zero indicates that an event will not occur. Likewise, probabilities expressed as percentages possess values between zero and one hundred percent where probabilities closer to zero are unlikely to occur and those close to one hundred percent are more likely to occur.

Now, we will start by constructing a table. The question presents data associated with two different types of variables: grade level and class. There are four grade levels (i.e. freshman, sophomores, juniors, and seniors) and four elective science classes (i.e. astronomy, ecology, physics, and chemistry). We need to make a table that has four rows and four columns. Next, we can input the data contained in the table. Last we will add up each row and column in order to gain totals for each variable. If you have done this properly, then you should have created a table similar to the following:

After, the two-way table has been constructed you can then use it to solve the question: what is the probability that a senior will take astronomy?

First, we need to create the following ratio: number seniors planning to take the astrology class to the total number of seniors.

Substitute values using the table and solve.

### Example Question #9 : Two Way Frequency Tables: Ccss.Math.Content.Hss Cp.A.4

A high school wants to assess the science elective courses that its students have chosen for their next year of education. Five freshmen, thirty-four sophomores, nine juniors, and forty-four seniors chose to take astronomy. Eighteen freshmen, twenty-four sophomores, thirty-three juniors, and twenty seniors are planning to take ecology. Twelve freshmen, thirty-eight sophomores, eighteen juniors, and twenty-five seniors want to take physics. Last, four freshmen, fourteen sophomores, fifteen juniors, and twenty-eight seniors chose to take chemistry.

Use this information to create a two-way frequency table and calculate the probability that a senior will take astronomy.

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

Let's use a simple example: the rolling of a die. We want to know the probability of rolling a one. We know that the sample space is six because there are six sides or outcomes to the die. Also, we know that there is only a single side with a value of one; therefore,

Now, let's convert this into a percentage:

Probabilities expressed in fraction form will have values between zero and one. One indicates that an event will definitely occur, while zero indicates that an event will not occur. Likewise, probabilities expressed as percentages possess values between zero and one hundred percent where probabilities closer to zero are unlikely to occur and those close to one hundred percent are more likely to occur.

Now, we will start by constructing a table. The question presents data associated with two different types of variables: grade level and class. There are four grade levels (i.e. freshman, sophomores, juniors, and seniors) and four elective science classes (i.e. astronomy, ecology, physics, and chemistry). We need to make a table that has four rows and four columns. Next, we can input the data contained in the table. Last we will add up each row and column in order to gain totals for each variable. If you have done this properly, then you should have created a table similar to the following:

After, the two-way table has been constructed you can then use it to solve the question: what is the probability that a senior will take astronomy?

First, we need to create the following ratio: number seniors planning to take the astrology class to the total number of seniors.

Substitute values using the table and solve.

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