SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Shade the Venn diagram to represent the set. 1) B A 1) 2) (A B C')' 2) Determine whether the given events are mutually exclusive. 3) Going to the beach and staying home at 2 pm on your birthday 3) Find the odds. 4) Find the odds in favor of drawing a 5 when a card is drawn at random from the cards pictured below. 4) Find the number of subsets of the set. 5) {0} 5) Find the probability. 6) If two cards are drawn with replacement from an ordinary deck, find the probability the first card is a heart and the second is a diamond. 6) 7) A bag contains 5 red marbles, 3 blue marbles, and 7 green marbles. What is the probability that a randomly selected marble is blue? 7) 8) Assuming that boy and girl babies are equally likely, find the probability that a family with four children has all boys given that at least one is a boy. 8) Insert " " or " " in the blank to make the statement true. 9) {x x is a counting number larger than 5} {7, 8, 9,... } 9) Use a Venn diagram to find the indicated probability. 10) If P(A B) = 0.65, P(A) = 0.32, and P(B) = 0.44, find P(A B). 10) 1

2 Use a Venn diagram to answer the question. 11) A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 750 responses with the following results: 225 were interested in an interview show and a documentary, but not reruns; 30 were interested in an interview show and reruns, but not a documentary; 105 were interested in reruns but not an interview show; 180 were interested in an interview show but not a documentary; 75 were interested in a documentary and reruns; 45 were interested in an interview show and reruns; 60 were interested in none of the three. How many are interested in exactly one kind of show? 11) Use a Venn Diagram and the given information to determine the number of elements in the indicated region. 12) n(u) = 103, n(a) = 47, n(b) = 42, n(c) = 33, n(a B) = 10, n(a C) = 6, n(b C) = 8. Find 12) n(a (B C)). Use Bayes' rule to find the indicated probability. 13) Two shipments of components were received by a factory and stored in two separate bins. Shipment I has 2% of its contents defective, while shipment II has 5% of its contents defective. If it is equally likely an employee will go to either bin and select a component randomly, what is the probability that a defective component came from shipment II? 13) Use the union rule to answer the question. 14) If n(b) = 48, n(a B) = 9, and n(a B) = 84; what is n(a)? 14) Find the indicated probability. 15) The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement. 15) Age at Retirement Over 65 Total Attorney College Professor Administrative Assistant Store Clerk Total Suppose one of these people is selected at random. Compute the probability that the person selected was an attorney who retired between 61 and 65. 2

3 16) The following contingency table shows the popular votes cast in the 1984 presidential election by region and political party. Round your answer to three decimal places. 16) Political Party Region Democratic Republican Other Northeast , Midwest 10,511 14, South 10,998 17, West , Totals 37,577 54, A person who voted Democratic in the 1984 presidential election is selected at random. Find the probability that the person was from the West. 17) Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that one marble is green, and one marble is red. 17) Let U = {q, r, s, t, u, v, w, x, y, z}; A = {q, s, u, w, y}; B = {q, s, y, z}; and C = {v, w, x, y, z}. List the members of the indicated set, using set braces. 18) A B' 18) Tell whether the statement is true or false. 19) {56, 57, 56, 57} = {56, 57} 19) Let A = { 6, 4, 1, {3, 0, 8}, {9} }. Determine whether the statement is true or false. 20) 3 A 20) Find the number of elements in the indicated set by referring to the given table. 21) The table below shows the results of a poll taken in a U.S. city in which people are asked which candidate they intend to vote for in an upcoming presidential election. 21) NonHispanic White (A) African- (C) Asian (E) Indian (F) Hispanic (B) Democrat (D) Republican (R) Other (O) Totals Find the number of people in the set R F Decide whether the statement is true or false. 22) {4, 6, 8} {5, 7, 8} = {4, 6, 8, 5, 7} 22) Write the sample space for the given experiment. 23) A box contains 2 blue cards numbered 1 through 2, and 3 green cards numbered 1 through 3. A blue card is picked, followed by a green card. 23) 3

4 Use the rule of total probability to find the indicated probability. 24) 31% of the workers at Motor Works are female, while 57% of the workers at City Bank are female. If one of these companies is selected at random (assume a chance for each), and then a worker is selected at random, what is the probability that the worker will be female? 24) Use a Venn diagram to decide if the statement is true or false. 25) (A B) (A C) = A (B C) 25) Identify the probability statement as empirical or not. 26) The probability that it will snow on December 25 in New York City is ) Use the given table to find the indicated probability. 27) People in a survey were given three choices of soft drinks and asked to choose one favorite. The following table shows the results. 27) cola root beer lemon-lime totals under 21 years of age between 21 and over 40 years of age One of the participants is selected at random. Find the probability that the person is over 40 and prefers cola. An experiment is conducted for which the sample space is S = {a, b, c, d}. Decide if the given probability assignment is possible for this experiment. If the assignment is not possible, tell why. 28) 28) Outcomes Probabilities a 0.13 b 0.36 c 0.10 d 0.41 Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; D = {2, 5, 8}; and U = {1, 2, 3, 4, 5, 6, 7, 8}. Determine whether the given statement is true or false. 29) A {7, 5, 3, 1} 29) 4

5 Solve the problem. 30) Steve lives in Tewin Wood, a wooded area prone to power outages during storms due to falling trees. The probability that there will be a storm tomorrow in Tewin Wood is If there is a storm, the probability that there will be a power outage is If there is no storm, there will not be a power outage. What is the probability that Steve will not have a power outage tomorrow? 30) 5