# Mathematics

Mathematics

1. Assume that an event A contains 10 observations and event B contains 15 observations. If the intersection of events A and B contains exactly 3 observations, how many observations are in the union of these two events?

A. 28

B. 10

C. 22

D. 0

2. Let event A = rolling a 1 on a die, and let event B = rolling an even number on a die. Which of the following is correct concerning these two events?

A. On a Venn diagram, event B would contain event A.

B. Events A and B are mutually exclusive.

C. On a Venn diagram, event A would overlap event B.

D. Events A and B are exhaustive.

3. From an ordinary deck of 52 playing cards, one is selected at random. What is the probability that the selected card is either an ace, a queen, or a three?

A. 0.3

B. 0.25

C. 0.0769

D. 0.2308

4. Which of the following is correct concerning the Poisson distribution?

A. The mean is usually larger than the variance.

B. The event being studied is restricted to a given span of time, space, or distance.

C. Each event being studied must be statistically dependent on the previous event.

D. The mean is usually smaller than the variance.

5. A breeder records probabilities for two variables in a population of animals using the two-way table given here. Let A be the event “shaggy and brown-haired.” Compute P(Ac).

Brown-haired BlondShort-haired 0.06 0.23

Shaggy 0.51 0.20

A. 0.36

B. 0.49

C. 0.77

D. 0.51

6. A credit card company decides to study the frequency with which its cardholders charge for items from a certain chain of retail stores. The data values collected in the study appear to be normally distributed with a mean of 25 charged purchases and a standard deviation of 2 charged purchases. Out of the total number of cardholders, about how many would you expect are charging 27 or more purchases in this study?

A. 47.8%

B. 94.8%

C. 68.3%

D. 15.9%

7. In the binomial probability distribution, p stands for the

A. probability of failure in any given trial.

B. number of trials.

C. number of successes.

D. probability of success in any given trial.

8. The Burger Bin fast-food restaurant sells a mean of 24 burgers an hour and its burger sales are normally distributed. The standard deviation is 3.061. What is the probability that the Burger Bin will sell 12 to 18 burgers in an hour?

A. 0.342

B. 0.475

C. 0.136

D. 0.239

9. Consider an experiment that results in a positive outcome with probability 0.38 and a negative outcome with probability 0.62. Create a new experiment consisting of repeating the original experiment 3 times. Assume each repetition is independent of the others. What is the probability of three successes?

A. 1.14

B. 0.238

C. 0.762

D. 0.055

10. An apartment complex has two activating devices in each fire detector. One is smoke-activated and has a probability of .98 of sounding an alarm when it should. The second is a heat-sensitive activator and has a probability of .95 of operating when it should. Each activator operates independently of the other. Presume a fire starts near a detector. What is the probability that both activating devices will work properly?

A. 0.049

B. 0.9895C. 0.931

D. 0.965

11. Each football game begins with a coin toss in the presence of the captains from the two opposing teams. (The winner of the toss has the choice of goals or of kicking or receiving the first kickoff.) A particular football team is scheduled to play 10 games this season. Let x = the number of coin tosses that the team captain wins during the season. Using the appropriate table in your textbook, solve for P(4 ≤ x ≤8).

A. 0.817

B. 0.377

C. 0.246

D. 0.171

12. The probability of an offender having a speeding ticket is 35%, having a parking ticket is 44%, having both is 12%. What is the probability of an offender having either a speeding ticket or a parking ticket or both?

A. 67%

B. 79%

C. 55%

D. 91%

13. For each car entering the drive-through of a fast-food restaurant, x = the number of occupants. In this study, x is a

A. joint probability.

B. discrete random variable.

C. continuous quantitative variable.

D. dependent event.

14. A basketball team at a university is composed of ten players. The team is made up of players who play the position of either guard, forward, or center. Four of the ten are guards, four are forwards, and two are centers. The numbers that the players wear on their shirts are 1, 2, 3, and 4 for the guards; 5, 6, 7, and 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a

player be selected at random from the ten. The events are defined as follows:

Let A be the event that the player selected has a number from 1 to 8.

Let B be the event that the player selected is a guard.

Let C be the event that the player selected is a forward.

Let D be the event that the player selected is a starter.

Let E be the event that the player selected is a center.

Calculate P(C).

A. 0.20

B. 0.40C. 0.50

D. 0.80

Protestant Catholic Jewish Other

Democrat 0.35 0.10 0.03 0.02

Republican 0.27 0.09 0.02 0.01

Independent 0.05 0.03 0.02 0.01

15. The table above gives the probabilities of combinations of religion and political parties in a city in the United States. What is the probability that a randomly selected person will be a Protestant and at the same time be a Democrat or a Republican?

A. 0.89

B. 0.62

C. 0.67

D. 0.35

16. A breeder records probabilities for two variables in a population of animals using the two-way table given here. Given that an animal is brown-haired, what is the probability that it’s short-haired?

Brown-haired Blond

Short-haired 0.06 0.23

Shaggy 0.51 0.20

A. 0.0306

B. 0.222

C. 0.105

D. 0.06

17. Which of the following is a discrete random variable?

A. The weight of football players in the NFL

B. The time required to drive from Dallas to Denver

C. The average daily consumption of water in a household

D. The number of three-point shots completed in a college basketball game

18. Find the z-score that determines that the area to the right of z is 0.8264.

A. 0.94

B. –1.36

C. –0.94

D. 1.36

19. Tornadoes for January in Kansas average 3.2 per month. What is the probability that, next January, Kansas will experience exactly two tornadoes?End of exam

A. 0.4076

B. 0.2087

C. 0.2226

D. 0.1304

20. If event A and event B are mutually exclusive, P(A or B) =

A. P(A) + P(B).

B. P(A) + P(B) – P(A and B).

C. P(A) – P(B).

D. P(A + B).