#1. (1pt each) Determine whether each statement is true or false.

(a) When two events are mutually exclusive, P(A or B) = P(A) + P(B) - P(A and B).

(b) When two events are dependent, they must have the same probability of occurring.

(c) An event and its complement cannot occur at the same time.

(d) The arrangement ABC is the same as BCA for permutation.

(e) When objects are arranged in a specific order, the arrangement is called a permutation.

#2. (2pts) The probability that an event happens is 0.42. What is the probability that the event won't happen?

#3. (1pt) The complement of guessing 5 correct answers on a 5-question true/false exam is

(a) Guessing 5 incorrect answers. (b) Guessing at least 4 correct answers. (c) Guessing at most 4 correct answers. (d) Guessing no incorrect answers.

#4. (2pts each) Calculate (a) 11P2

(b) 9C7

(c) 56!

(60 - 5)!

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#5. (1pt each) Complete the following statements with the best answer. (a) The set of all possible outcomes of a probability experiment is called the .

(b) The probability of an event can be any number between and including and .

(c) If an event cannot occur, its probability is .

(d) The sum of the probabilities of the events in the sample space is .

(e) When two events cannot occur at the same time, they are said to be .

#6. (2pts) Identify the sample space of the probability experiment and determine the number of outcomes in the event.

Experiment: Choosing a month of the year. Event: Choosing a month that begins with the letter J.

#7. (1pt each) Classify the statement as an example of classical probability, empirical probability, or subjective probability.

(a) On the basis of prior counts, a quality control officer says there is a 0.05 probability that a randomly chosen part is defective.

(b) The probability of randomly selecting five cards of the same suit from a standard deck is about 0.0005.

(c) The chance that Corporation A's stock price will fall today is 75%.

#8. (3pts each) Decide if the events are mutually exclusive. Explain your reasoning.

(a) Event A: Randomly select a red jelly bean from a jar.

Event B: Randomly select a yellow jelly bean from the same jar.

(b) Event A: Randomly select a person who loves cats.

Event B: Randomly select a person who owns a dog.

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#9. (2pts) You are given that P(A) = 0.35 and P(B) = 0.25. Do you have enough information to find P(A and B). Explain.

#10. (2pts) You are given that P(a) = 0.15 and P(B) = 0.40. Do you have enough information to find P(A or B). Explain.

#11. (4pts) You are shopping, and your roommate has asked you to pick up toothpaste and dental rinse. However, your roommate did not tell you which brands to get.The store has eight brands of toothpaste and five brands of dental rinse. What is the probability that you will purchase the correct brands of both products? Is this an unusual event? Explain.

#12. (2pts each) An experiment results in one of three mutually exclusive events A, B and C. It is known that P(A)=0.3,P(B)=0.55 and P(C)=0.15. Find each of the following probabilities:

(a) Find P(A and C).

(b) Find P(B < C).

(c) Find P(B or A).

#13. (1pt each) An individual stock is selected at random from the portfolio represented by the box-and-whisker plot shown.

Find the probability that the stock price is

(a) greater than $21.

(b) between $30 and $94.

(c) $12 or more.

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#14. (3pts each) A batch of 200 calculators contains 3 defective units. What is the proba- bility that a sample of three calculators will have

(a) no defective calculators?

(b) all defective calculators?

(c) at least one defective calculators?

#15. (3pts) Fifteen cyclists enter a race. In how many ways can they finish first, second, and third?

#16. (3pts) An employer must hire 2 people from a list of 13 applicants. In how many ways can the employer choose to hire the 2 people?

#17. (3pts each) The table shows the number (in thousands) of earned degrees, by level and gender, conferred in the United States in a recent year. (Source: U.S. National Center for Education Statistics)

A person who earned a degree in the year is randomly selected. Find the probability of selecting someone who (a) earned a doctoral degree.

(b) earned a doctoral degree given that the person is a male.

(c) earned an associate's degree or a doctoral degree.

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(d) is a male given that the person earned associate's degree.

#18. (4pts) A security code consists of three letters followed by one digit.The first letter cannot be an A, B, or C. What is the probability of guessing the security code in one trial?

#19. (1pt each) Identify the following random variables as discrete or continuous.

(a) The number of books in a university library.

(b) the number of tornadoes in the month of June in Oklahoma.

(c) The volume of blood drawn for a blood test.

#20. (3pts each) Explain why each of the following is or not a valid probability distribution for a discrete random variable x:

(a)

x 0 1 2 3 p(x) 0.2 0.3 0.3 0.2

(b)

x 0 -1 3 p(x) 0.25 0.5 0.2

#21. (2pts each) According to an Associated Pressn Petside.com poll, half of all pets owners would get their next dog or cat from a shelter. Consider a random sample of 10 owners and define x as the number of pet owners who would acquire their next dog or cat from a shelter. Assume that x is a binomial random variable.

(a) For this binomial experiment, define a success.

(b) For this binomial experiment, what is n?

(c) For this binomial experiment, what is p?5

(d) Find p(7).

#22. (8pts) In Pittsburgh, Pennsylvania, about 56% of the days in a year are cloudy. Find the mean, variance, and standard deviation for the number of cloudy days during the month of June.

#23. (4pts) The mean age of the 27 men in the Sparkesville Bridge club is 57.8 years. The mean age of the 25 women in the club is 52.4 years. What is the mean age of all 52 members?

#24. (6pts) The East Coast Independent News periodically runs ads in its own classified section offering a months free subscription to those who respond. In this way, management can get a sense about the number of subscribers who read the classified section each day. Over a period of 2 years, careful records have been kept. The mean number of responses per ad is x =525 with standard deviation s = 30.

(a) Determine a Chebyshev interval about the mean in which at least 88.9% of the data fall.

(b) Using the empirical rule, find the interval that contains 68% of the data.

#25. (3pts) The average of the number of trials it took a sample of mice to learn to traverse a maze was 12. The standard deviation was 3. Using Chebyshev's Theorem, find the minimum percentage of data values that will fall in the interval of 4 - 20.