1. Determine which numbers could not be used to represent the probability of an event.

Select all that apply:

A. 33.3%, because probability values cannot be greater than 1.

B. 64/25 , because probability values cannot be greater than 1.

C. 0, because probability values must be greater than 0.

D. 0.0002, because probability values must be rounded to two decimal places.

E. 320/1058, because the probability values cannot be in fraction form.

F. 1.5 , because probability values cannot be less than 0.

2. Explain why the statement is incorrect. The probability of rain tomorrow is 135%.

What makes the statement incorrect?

A. The probability of an event must be contained in the interval [0,100].

B. The probability of an event cannot exceed 100%.

C. The chance of rain is always more than 100%.

D. An event needs to have more than one possible outcome.

3. Classify the following statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.

The probability of choosing 5 numbers from 1 to 57 that match the numbers drawn by a certain lottery is 1/4187106 =0.00000024.

This is an example of __________ probability, since _________________________________.

4. Classify the following statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.

According to company records, the probability that a washing machine will needs repairs during a nine-year period is 0.28.

This is an example of __________ probability, since ________________________________________.

5. Determine whether the following events are mutually exclusive. Explain your reasoning.

Event A: Randomly select a male psychology major.

Event B: Randomly select a psychology major who is 21 years old.

These events _____ mutually exclusive, since _________________________.

6. Determine whether the following events are mutually exclusive. Explain your reasoning.

Event A: Randomly select a voter who legally voted for the President in South Carolina.

Event B: Randomly select a voter who legally voted for the President in Texas.

These events _____ mutually exclusive, since it is _____ possible for a voter to both have legally voted for the President in South Carolina and _____ legally voted for the President in Texas.

7. For the given pair of events, classify the two events as independent or dependent.

Randomly selecting a city in Texas.

Randomly selecting a county in Texas.

Choose the correct answer below:

- The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.

- The two events are dependent because the occurrence of one does not affect the probability of the occurrence of the other.

- The two events are dependent because the occurrence of one affects the probability of the occurrence of the other.

- The two events are independent because the occurrence of one affects the probability of the occurrence of the other.

8. Determine whether the events are independent or dependent. Explain your reasoning.

Returning a rented movie after the due date and receiving a late fee.

The events are __________ because the outcome of returning the rented movie after the due date _____ the probability of the outcome of receiving a late fee.

9. A probability event consists of rolling a fair 10-sided die. Find the probability of the event below: rolling a number greater than 7

The probability is _____.

10. Two of the 100 digital video records (DVRs) in an inventory are known to be defective. What is the probability you randomly select a DVR that is not defective?

The probability is _____.

11. Use the frequency distribution, which shows the number of American voters (in millions) according to age, to find the probability that a voter chosen at random is in the 18 to 10 year old age range.

Ages: 18 to 20 21 to 24 25 to 34 35 to 44 45 to 64 65 and over

Frequency: 5.6 8.7 23.7 22.7 51.5 27.3

The probability that a voter chosen at random is in the 18 to 20 year old range is _______.

12. Two cards are randomly selected from a deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a heart and then selecting a diamond.

The probability of selecting a heart and then selecting a diamond is __________.

13. A coin is tossed, and an eight-sided die numbered 1 through 8 is rolled. Find the probability of tossing a tail and then rolling a number greater than 6.

The probability of tossing a tail and then rolling a number greater than 6 is _______.

15. In a certain lottery, you must correctly select 6 numbers (in any order) out of 37 to win. You purchase one lottery ticket. What's the probability that you will win?

The probability of winning is __________.

16. A class has 32 students. In how many different ways can six students form a group for an activity? (Assume the order of the students is not important.)

There are __________ different ways that the six students can form a group for an activity.

17. A DJ is preparing a playlist of 17 songs. How many different ways can the DJ arrange the first four songs on the playlist?

There are _____ different ways that the DJ can arrange the first four songs on a playlist.

18. A warehouse employs 22 workers on the first shift, 17 workers on the second shift, and 13 workers on the third shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing exactly two second shift workers and two third shift workers.

The probability of choosing two second shift workers and two third shift workers is _____.

19. How many 10-letter words (real or imaginary) can be formed from the following letters?

E, L, O, Q, X, A, S, L, R, Q

_____ ten-letter words (real or imaginary) can be formed with the given letters.

20. The number of dogs per household in a small town.

Dogs: 1 2 3 4 5

Probability: 0.651 0.220 0.085 0.013 0.009

Complete parts (a) and (b) below.

a. Find the mean, variance and standard deviation of the probability distribution.

The mean of the probability distribution:

Find the variance of the probability distribution:

Find the standard deviation of the probability distribution:

b. Interpret the results in the context of the real-life situation.

A. A household on average has 0.6 dog with a standard deviation of 0.9 dog.

B. A household on average has 0.6 dog with a standard deviation of 17 dogs.

C. A household on average has 0.9 dog with a standard deviation of 0.9 dog.

D. A household on average has 0.9 dog with a standard deviation of 0.6 dog.

21. 38% of likely U.S. voters think that the federal government should get more involved in fighting local crime. You randomly select six likely U.S. voters and ask them whether they think the government should be more involved in fighting local crime. The random variable represents the number of likely U.S. voters who think that the federal government should get more involved in fighting local crime.

a. Find the mean of the binomial distribution:

b. Find the variance of the binomial distribution:

c. Find the standard deviation of the binomial distribution:

d. Interpret the results in the context of the real-life situation:

In most samples of 6 U.S. voters, the number of voters who think that the federal government should get more involved in local crime and would differ by no more than _____.

22. 63% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is:

(a) exactly 5, (b) at least 6, (c) less than four.

a. P(5)=

b. P(x>6)=

c. P(x<4)=

23. Find the area of the indicated region under the standard normal curve: The area between z=1.4 andz=1.3.

The area between z=1.4 and z=1.3 under the standard normal curve is __________.

24. In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean height of 68.3 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below.

a. Find the probability that a study participant is has a height that is less than 66 inches.

The probability that a study participant is has a height that is less than 66 inches tall is _____.

b. Find the probability that a study participant is has a height that is between 66 and 71 inches.

The probability that a study participant is has a height that is between 66 and 71 inches tall is _____.

c. Find the probability that a study participant has a height that is more than 71 inches.

The probability that a study participant has a height that is more than 71 inches tall is _____.

d. Identify any unusual events. Explain your reasoning. Choose the correct answer below.

A. There are no unusual events because all probabilities are greater than 0.05.

B. The event in part (a) is unusual because its probability is less than 0.05.

C. The events in parts (a), (b), and (c) are unusual because all their probabilities are less than 0.05.

D. The events in parts (a) and (c) are unusual because its probabilities are less than 0.05.