### All Common Core: High School - Statistics and Probability Resources

## Example Questions

### Example Question #1 : Making Inferences & Justifying Conclusions

Two college students, Joe and Melissa, are playing a tabletop role-playing game where snake eyes (a value of one on each of the two dice) allows one opponent to effectively attack the other. After three turns, Joe roles snake eyes three times consecutively while Melissa has not rolled it once. She begins to believe that Joe is using loaded dice, which would give him an unfair advantage. She decides to test this theory by rolling her fair dice three times in a row for sixty trials. Melissa knows that the probability of rolling snake eyes is fairly low; furthermore, after sixty trials she only roles snake eyes two times in a row.

Which of the following will Melissa most likely conclude?

**Possible Answers:**

Joe is using fair dice

Joe has tricked her by using loaded dice

Melissa cannot tell if Joe is using loaded or fair dice

Melissa miscalculated the probability of rolling snake eyes

**Correct answer:**

Joe has tricked her by using loaded dice

This question is asking us to use a simulation in order to determine whether or not an observed phenomenon is statistically probable. We will do this by creating and testing a hypothesis. Afterwards, we can use our collected data to make a conclusion as to whether or not Joe is using fair dice in this scenario.

Hypotheses are "if/then" statements that represent an inference or educated guess regarding a particular phenomenon. They are tested through experimentation. The results of an experiment will reveal if a hypothesis can be supported or not. At this point, it is important tot note that a hypothesis can never be proven: experimentation can only support or refute a hypothesis. Even scientific theories cannot be proven they only have a mass of supporting studies to add to their scientific validity.

Before we solve this problem, we should review the scientific process. In the scientific method we observe a phenomenon, gather background information, develop a tentative explanation (i.e. a hypothesis), test this explanation through the observation and manipulation of variables, and, finally, we create conclusions based upon experimentation. These conclusions will either support or refute the hypothesis.

Now, let's use this information to solve the problem regarding whether or not Joe is using fair dice. In this problem, Melissa noticed that Joe rolled snake eyes three times in a row. She gathered background information and identified the following probability calculations:

From this information, she realized that the probability of rolling snake eyes three times in a row is very low. Using this information, Melissa created an experiment, In this experiment, she rolled her known fair dice three times in a row for sixty trials. In these sixty trials she was only able to roll snake eyes in a row two times. From this information she was able to make the following conclusion: "Joe has tricked her by using loaded dice."

In this lesson we have learned how to use simulations and the scientific method in order to determine whether or not an event is the product of random chance or manipulation (i.e. Joe tricking Melissa with loaded dice).

### Example Question #2 : Making Inferences & Justifying Conclusions

Two college students, Joe and Melissa, are playing a tabletop role-playing game where snake eyes (a value of one on each of the two dice) allows one opponent to effectively attack the other. After three turns, Joe roles snake eyes three times while Melissa has not rolled it once. She begins to believe that Joe is using loaded dice, which would give him an unfair advantage. She decides to test this theory by rolling her fair dice three times in a row for sixty trials. Melissa knows that the probability of rolling snake eyes is fairly low; furthermore, after sixty trials she only roles snake eyes two times in a row.

Which of the following will Melissa most likely conclude?

**Possible Answers:**

Melissa miscalculated the probability of rolling snake eyes

Melissa cannot tell if Joe is using loaded or fair dice

Joe has tricked her by using loaded dice

Joe is using fair dice

**Correct answer:**

Joe has tricked her by using loaded dice

This question is asking us to use a simulation in order to determine whether or not an observed phenomenon is statistically probable. We will do this by creating and testing a hypothesis. Afterwards, we can use our collected data to make a conclusion as to whether or not Joe is using fair dice in this scenario.

Hypotheses are "if/then" statements that represent an inference or educated guess regarding a particular phenomenon. They are tested through experimentation. The results of an experiment will reveal if a hypothesis can be supported or not. At this point, it is important tot note that a hypothesis can never be proven: experimentation can only support or refute a hypothesis. Even scientific theories cannot be proven they only have a mass of supporting studies to add to their scientific validity.

Before we solve this problem, we should review the scientific process. In the scientific method we observe a phenomenon, gather background information, develop a tentative explanation (i.e. a hypothesis), test this explanation through the observation and manipulation of variables, and, finally, we create conclusions based upon experimentation. These conclusions will either support or refute the hypothesis.

Now, let's use this information to solve the problem regarding whether or not Joe is using fair dice. In this problem, Melissa noticed that Joe rolled snake eyes three times in a row. She gathered background information and identified the following probability calculations:

From this information, she realized that the probability of rolling snake eyes three times in a row is very low. Using this information, Melissa created an experiment, In this experiment, she rolled her known fair dice three times in a row for sixty trials. In these sixty trials she was only able to roll snake eyes in a row two times. From this information she was able to make the following conclusion: "Joe has tricked her by using loaded dice."

In this lesson we have learned how to use simulations and the scientific method in order to determine whether or not an event is the product of random chance or manipulation (i.e. Joe tricking Melissa with loaded dice).

### Example Question #3 : Making Inferences & Justifying Conclusions

Two college students, Joe and Melissa, are playing a tabletop role-playing game where snake eyes (a value of one on each of the two dice) allows one opponent to effectively attack the other. After five turns Joe roles snake eyes five times consecutively while Melissa has not rolled it once. She begins to believe that Joe is using loaded dice, which would give him an unfair advantage. She decides to test this theory by rolling her fair dice five times in a row for sixty trials. Melissa knows that the probability of rolling snake eyes is fairly low; furthermore, after sixty trials she only roles snake eyes two times in a row.

Which of the following will Melissa most likely conclude?

**Possible Answers:**

Joe is using fair dice

Melissa cannot tell if Joe is using loaded or fair dice

Joe has tricked her by using loaded dice

Melissa miscalculated the probability of rolling snake eyes

**Correct answer:**

Joe has tricked her by using loaded dice

This question is asking us to use a simulation in order to determine whether or not an observed phenomenon is statistically probable. We will do this by creating and testing a hypothesis. Afterwards, we can use our collected data to make a conclusion as to whether or not Joe is using fair dice in this scenario.

Hypotheses are 'if/then' statements that represent an inference or educated guess regarding a particular phenomenon. They are tested through experimentation. The results of an experiment will reveal if a hypothesis can be supported or not. At this point, it is important tot note that a hypothesis can never be proven: experimentation can only support or refute a hypothesis. Even scientific theories cannot be proven they only have a mass of supporting studies to add to their scientific validity.

Before we solve this problem, we should review the scientific process. In the scientific method we observe a phenomenon, gather background information, develop a tentative explanation (i.e. a hypothesis), test this explanation through the observation and manipulation of variables, and, finally, we create conclusions based upon experimentation. These conclusions will either support or refute the hypothesis.

Now, let's use this information to solve the problem regarding whether or not Joe is using fair dice. In this problem, Melissa noticed that Joe rolled snake eyes three times in a row. She gathered background information and identified the following probability calculations:

From this information, she realized that the probability of rolling snake eyes five times in a row is very low. Using this information, Melissa created an experiment, In this experiment, she rolled her known fair dice five times in a row for sixty trials. In these sixty trials she was only able to roll snake eyes in a row two times. From this information she was able to make the following conclusion: 'Joe has tricked her by using loaded dice.'

In this lesson we have learned how to use simulations and the scientific method in order to determine whether or not an event is the product of random chance or manipulation (i.e. Joe tricking Melissa with loaded dice).

### Example Question #4 : Making Inferences & Justifying Conclusions

Two college students, Joe and Melissa, are playing a tabletop role-playing game where snake eyes (a value of one on each of the two dice) allows one opponent to effectively attack the other.After four turns Joe roles snake eyes four times consecutively while Melissa has not rolled it once. She begins to believe that Joe is using loaded dice, which would give him an unfair advantage.She decides to test this theory by rolling her fair dice four times in a row for sixty trials. Melissa knows that the probability of rolling snake eyes is fairly low; furthermore, after sixty trials she only roles snake eyes two times in a row.

Which of the following will Melissa most likely conclude?

**Possible Answers:**

Melissa miscalculated the probability of rolling snake eyes

Joe is using fair dice

Joe has tricked her by using loaded dice

Melissa cannot tell if Joe is using loaded or fair dice

**Correct answer:**

Joe has tricked her by using loaded dice

Hypotheses are 'if/then' statements that represent an inference or educated guess regarding a particular phenomenon. They are tested through experimentation. The results of an experiment will reveal if a hypothesis can be supported or not. At this point, it is important tot note that a hypothesis can never be proven: experimentation can only support or refute a hypothesis. Even scientific theories cannot be proven they only have a mass of supporting studies to add to their scientific validity.

From this information, she realized that the probability of rolling snake eyes four times in a row is very low. Using this information, Melissa created an experiment, In this experiment, she rolled her known fair dice four times in a row for sixty trials. In these sixty trials she was only able to roll snake eyes in a row two times. From this information she was able to make the following conclusion: 'Joe has tricked her by using loaded dice.'

### Example Question #5 : Making Inferences & Justifying Conclusions

Two college students, Joe and Melissa, are playing a tabletop role-playing game where snake eyes (a value of one on each of the two dice) allows one opponent to effectively attack the other. After six turns Joe roles snake eyes six times consecutively while Melissa has not rolled it once. She begins to believe that Joe is using loaded dice, which would give him an unfair advantage. She decides to test this theory by rolling her fair dice six times in a row for sixty trials. Melissa knows that the probability of rolling snake eyes is fairly low; furthermore, after sixty trials she only roles snake eyes two times in a row.

Which of the following will Melissa most likely conclude?

**Possible Answers:**

Joe has tricked her by using loaded dice

Melissa miscalculated the probability of rolling snake eyes

Joe is using fair dice

Melissa cannot tell if Joe is using loaded or fair dice

**Correct answer:**

Joe has tricked her by using loaded dice

Hypotheses are 'if/then' statements that represent an inference or educated guess regarding a particular phenomenon. They are tested through experimentation. The results of an experiment will reveal if a hypothesis can be supported or not. At this point, it is important tot note that a hypothesis can never be proven: experimentation can only support or refute a hypothesis. Even scientific theories cannot be proven they only have a mass of supporting studies to add to their scientific validity.

From this information, she realized that the probability of rolling snake eyes six times in a row is very low. Using this information, Melissa created an experiment, In this experiment, she rolled her known fair dice six times in a row for sixty trials. In these sixty trials she was only able to roll snake eyes in a row two times. From this information she was able to make the following conclusion: 'Joe has tricked her by using loaded dice.'

### Example Question #1 : Making Inferences & Justifying Conclusions

Two college students, Joe and Melissa, are playing a tabletop role-playing game where snake eyes (a value of one on each of the two dice) allows one opponent to effectively attack the other. After seven turns Joe roles snake eyes seven times consecutively while Melissa has not rolled it once. She begins to believe that Joe is using loaded dice, which would give him an unfair advantage. She decides to test this theory by rolling her fair dice seven times in a row for sixty trials. Melissa knows that the probability of rolling snake eyes is fairly low; furthermore, after sixty trials she only roles snake eyes two times in a row.

Which of the following will Melissa most likely conclude?

**Possible Answers:**

Melissa miscalculated the probability of rolling snake eyes

Joe has tricked her by using loaded dice

Joe is using fair dice

Melissa cannot tell if Joe is using loaded or fair dice

**Correct answer:**

Joe has tricked her by using loaded dice

From this information, she realized that the probability of rolling snake eyes seven times in a row is very low. Using this information, Melissa created an experiment, In this experiment, she rolled her known fair dice seven times in a row for sixty trials. In these sixty trials she was only able to roll snake eyes in a row two times. From this information she was able to make the following conclusion: 'Joe has tricked her by using loaded dice.'

### Example Question #7 : Making Inferences & Justifying Conclusions

Two college students, Joe and Melissa, are playing a tabletop role-playing game where snake eyes (a value of one on each of the two dice) allows one opponent to effectively attack the other. After eight turns Joe roles snake eyes eight times consecutively while Melissa has not rolled it once. She begins to believe that Joe is using loaded dice, which would give him an unfair advantage. She decides to test this theory by rolling her fair dice eight times in a row for sixty trials. Melissa knows that the probability of rolling snake eyes is fairly low; furthermore, after sixty trials she only roles snake eyes two times in a row.

Which of the following will Melissa most likely conclude?

**Possible Answers:**

Joe is using fair dice

Melissa miscalculated the probability of rolling snake eyes

Joe has tricked her by using loaded dice

Melissa cannot tell if Joe is using loaded or fair dice

**Correct answer:**

Joe has tricked her by using loaded dice

From this information, she realized that the probability of rolling snake eyes eight times in a row is very low. Using this information, Melissa created an experiment, In this experiment, she rolled her known fair dice eight times in a row for sixty trials. In these sixty trials she was only able to roll snake eyes in a row two times. From this information she was able to make the following conclusion: 'Joe has tricked her by using loaded dice.'

### Example Question #1 : Making Inferences & Justifying Conclusions

Two college students, Joe and Melissa, are playing a tabletop role-playing game where snake eyes (a value of one on each of the two dice) allows one opponent to effectively attack the other. After nine turns Joe roles snake eyes nine times consecutively while Melissa has not rolled it once. She begins to believe that Joe is using loaded dice, which would give him an unfair advantage. She decides to test this theory by rolling her fair dice nine times in a row for sixty trials. Melissa knows that the probability of rolling snake eyes is fairly low; furthermore, after sixty trials she only roles snake eyes two times in a row.

Which of the following will Melissa most likely conclude?

**Possible Answers:**

Joe has tricked her by using loaded dice

Melissa miscalculated the probability of rolling snake eyes

Joe is using fair dice

Melissa cannot tell if Joe is using loaded or fair dice

**Correct answer:**

Joe has tricked her by using loaded dice

From this information, she realized that the probability of rolling snake eyes nine times in a row is very low. Using this information, Melissa created an experiment, In this experiment, she rolled her known fair dice nine times in a row for sixty trials. In these sixty trials she was only able to roll snake eyes in a row two times. From this information she was able to make the following conclusion: 'Joe has tricked her by using loaded dice.'

### Example Question #2 : Making Inferences & Justifying Conclusions

Two college students, Joe and Melissa, are playing a tabletop role-playing game where snake eyes (a value of one on each of the two dice) allows one opponent to effectively attack the other. After ten turns Joe roles snake eyes ten times consecutively while Melissa has not rolled it once. She begins to believe that Joe is using loaded dice, which would give him an unfair advantage. She decides to test this theory by rolling her fair dice ten times in a row for sixty trials. Melissa knows that the probability of rolling snake eyes is fairly low; furthermore, after sixty trials she only roles snake eyes two times in a row.

Which of the following will Melissa most likely conclude?

**Possible Answers:**

Melissa miscalculated the probability of rolling snake eyes

Joe has tricked her by using loaded dice

Melissa cannot tell if Joe is using loaded or fair dice

Joe is using fair dice

**Correct answer:**

Joe has tricked her by using loaded dice

From this information, she realized that the probability of rolling snake eyes ten times in a row is very low. Using this information, Melissa created an experiment, In this experiment, she rolled her known fair dice ten times in a row for sixty trials. In these sixty trials she was only able to roll snake eyes in a row two times. From this information she was able to make the following conclusion: 'Joe has tricked her by using loaded dice.'

### Example Question #1 : Simulations For Models: Ccss.Math.Content.Hss Ic.A.2

Two college students, Joe and Melissa, are playing a tabletop role-playing game where snake eyes (a value of one on each of the two dice) allows one opponent to effectively attack the other. After eleven turns Joe roles snake eyes eleven times consecutively while Melissa has not rolled it once. She begins to believe that Joe is using loaded dice, which would give him an unfair advantage. She decides to test this theory by rolling her fair dice eleven times in a row for sixty trials. Melissa knows that the probability of rolling snake eyes is fairly low; furthermore, after sixty trials she only roles snake eyes two times in a row.

Which of the following will Melissa most likely conclude?

**Possible Answers:**

Melissa miscalculated the probability of rolling snake eyes

Joe is using fair dice

Melissa cannot tell if Joe is using loaded or fair dice

Joe has tricked her by using loaded dice

**Correct answer:**

Joe has tricked her by using loaded dice

From this information, she realized that the probability of rolling snake eyes eleven times in a row is very low. Using this information, Melissa created an experiment, In this experiment, she rolled her known fair dice eleven times in a row for sixty trials. In these sixty trials she was only able to roll snake eyes in a row two times. From this information she was able to make the following conclusion: 'Joe has tricked her by using loaded dice.'

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