Question 1

Sometimes probabilities derived by the relative frequency method differ from the probabilities expected from classical probability methods. How does the law of large numbers apply in this situation?

Accepted Answer

The law of large numbers states that as an experiment is repeated again and again, the relative frequency probabilities tend to approach the actual probabilities expected from the classical approach.

Question 2

Compare the relative frequency formula for finding probabilities to the classical formula for finding probabilities. How are the two formulas similar and how are they different?
What special requirements does the classical approach have?

Accepted Answer

In the relative frequency formula, the probabilities are determined by conducting an experiment, counting the number of occurrences of the event, and creating the ratio of number of occurrences to number of times the experiment was conducted. In the classical approach, a sample space of all of the possible simple events is created and the number of successes is compared to the number of different simple events. In the classical approach, each outcome must be equally likely.

Question 3

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results.
-Assume that ten percent of us are left-handed. The probability of getting at least two left-handed people in a group of 7.

Accepted Answer

Answers may vary. Begin by representing left-handed people by the digit 0 and right-handed people by the other digits. Then use a calculator or computer program to generate 7 random integers. Count as a success if the last digit of two or more of the generated numbers is 0. Repeat for 100 trials. The estimated probability is the number of successes divided by 100. Estimated probability is about 0.26.

Question 4

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results.
-The probability of getting at least two boys in a family of seven children.

Accepted Answer

The answer of Use a graphing calculator to develop a...

Question 5

Discuss why the relative frequency method of computing probabilities might be chosen over the classical method.

Accepted Answer

The answer of Discuss why the relative frequency method of...

Question 6

Probabilities are useful in the decision-making process. Suppose a random sample of 152 students was surveyed regarding an instructor's teaching. Suppose 105 students rated the instructor either excellent or above average on lecture presentations, 96 students rated the instructor as giving difficult or very difficult assignments and tests. Would you take this instructor for a class? Discuss the influence of probabilities on making this decision.

Accepted Answer

The answer of Probabilities are useful in the decision-making process....

Question 7

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results.
-The probability of getting a total of 15 when four dice are thrown.

Accepted Answer

The answer of Use a graphing calculator to develop a...

Question 8

When asked about the probability that he would become a sumo wrestler, Sam replied "slim to none." Relate that phrase to a numeric probability and interpret his meaning.

Accepted Answer

The answer of When asked about the probability that he...

Question 9

Compare probabilities and odds. How can you convert odds to probabilities?

Accepted Answer

The answer of Compare probabilities and odds. How can you...

Question 10

If a game were "fair," the payoff on a bet would be the same as the odds for the event. In one game, the odds for winning are 1:13. If the game were "fair," what would the payoff be for a $5 bet? Of course, games in casinos are designed to make a profit for the casino investors. Supposing the casino makes the payoff at 1:11 odds, what profit does the casino make on your winning bet?

Accepted Answer

The answer of If a game were "fair," the payoff...

Question 11

On an exam on probability concepts, Sue had an answer of $\frac { 13 } { 8 }$ for one problem. Explain how she knew that this result was incorrect.

Accepted Answer

The answer of On an exam on probability concepts, Sue...

Question 12

Give an example of events which are independent but not disjoint.

Accepted Answer

The answer of Give an example of events which are...

Question 13

Tomorrow Freddy is playing in an important soccer game. He reasons that there are three possible outcomes (they could win, tie, or lose) so the probability of winning must be 1/3. Is this reasoning correct? Why or why not?

Accepted Answer

The answer of Tomorrow Freddy is playing in an important...

Question 14

List two reasons it is better to sample without replacement when testing batches of products. When sampling without replacement, should you use the multiplication rule for independent or dependent events? Explain your answer.

Accepted Answer

The answer of List two reasons it is better to...

Question 15

Describe an event whose probability of occurring is 1 and explain what that probability means. Describe an event whose probability of occurring is 0 and explain what that probability means.

Accepted Answer

The answer of Describe an event whose probability of occurring...

Question 16

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results.
-The probability of getting exactly three girls in a family of five children.

Accepted Answer

The answer of Use a graphing calculator to develop a...

Question 17

Which of the following cannot be a probability? 
A) 0

B) $\frac { 1 } { 2 }$

C) $- 1$

D) 1

Accepted Answer

Probabilities must be between 0 and 1, inclusive. Negative values cannot be probabilities.

Question 18

Which of the following cannot be a probability? 
A) $\frac { 2 } { 3 }$

B) $\frac { 3 } { 5 }$

C) $\frac { 5 } { 3 }$

D) $\frac { 1 } { 2 }$

Accepted Answer

Probabilities must be between 0 and 1, inclusive. $\frac{5}{3}$ is greater than 1, so it cannot be a probability.

Question 19

What important question must you answer before computing an "or" probability? How does the answer influence your computation?

Accepted Answer

The answer of What important question must you answer before...

Question 20

What important question must you answer before computing an "and" probability? How does the answer influence your computation?

Accepted Answer

The answer of What important question must you answer before...

Quiz 4: Probability

Sometimes probabilities derived by the relative frequency method differ from the probabilities expected from classical probability methods. How does the law of large numbers apply in this situation?

Compare the relative frequency formula for finding probabilities to the classical formula for finding probabilities. How are the two formulas similar and how are they different? What special requirements does the classical approach have?

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results. -Assume that ten percent of us are left-handed. The probability of getting at least two left-handed people in a group of 7.

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results. -The probability of getting at least two boys in a family of seven children.

Discuss why the relative frequency method of computing probabilities might be chosen over the classical method.

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results. -The probability of getting a total of 15 when four dice are thrown.

When asked about the probability that he would become a sumo wrestler, Sam replied "slim to none." Relate that phrase to a numeric probability and interpret his meaning.

Compare probabilities and odds. How can you convert odds to probabilities?

On an exam on probability concepts, Sue had an answer of 138\frac { 13 } { 8 }813​ for one problem. Explain how she knew that this result was incorrect.

Give an example of events which are independent but not disjoint.

Tomorrow Freddy is playing in an important soccer game. He reasons that there are three possible outcomes (they could win, tie, or lose) so the probability of winning must be 1/3. Is this reasoning correct? Why or why not?

List two reasons it is better to sample without replacement when testing batches of products. When sampling without replacement, should you use the multiplication rule for independent or dependent events? Explain your answer.

Describe an event whose probability of occurring is 1 and explain what that probability means. Describe an event whose probability of occurring is 0 and explain what that probability means.

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results. -The probability of getting exactly three girls in a family of five children.

Which of the following cannot be a probability?

Which of the following cannot be a probability?

What important question must you answer before computing an "or" probability? How does the answer influence your computation?

What important question must you answer before computing an "and" probability? How does the answer influence your computation?

On an exam on probability concepts, Sue had an answer of $\frac { 13 } { 8 }$ for one problem. Explain how she knew that this result was incorrect.