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

Transcription

1 Math 1324 Test 3 Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Insert " " or " " in the blank to make the statement true. 1) {18, 27, 32} {5, 27, 32, 42} Find the number of subsets of the set. 2) {math, English, history, science, art} 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. 3) (A B)' The lists below show five agricultural crops in Alabama, Arkansas, and Louisiana. Alabama Arkansas Louisiana soybeans (s) soybeans (s) soybeans (s) peanuts (p) rice (r) sugarcane (n) corn (c) cotton (t) rice (r) hay (h) hay (h) corn (c) wheat (w) wheat (w) cotton (t) Let U be the smallest possible universal set that includes all of the crops listed; and let A, K, and L be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set. 4) L' K' Shade the Venn diagram to represent the set. 5) (A B C')' Use a Venn Diagram and the given information to determine the number of elements in the indicated set. 6) n(u) = 60, n(a) = 31, n(b) = 19, and n(a B) = 4. Find n(a B)'. 1

2 Use a Venn diagram to answer the question. 7) 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 250 responses with the following results: 75 were interested in an interview show and a documentary, but not reruns; 10 were interested in an interview show and reruns, but not a documentary; 35 were interested in reruns but not an interview show; 60 were interested in an interview show but not a documentary; 25 were interested in a documentary and reruns; 15 were interested in an interview show and reruns; 20 were interested in none of the three. How many are interested in exactly one kind of show? Write the sample space for the given experiment. 8) 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. Find the probability of the given event. 9) A card drawn from a well-shuffled deck of 52 cards is an ace or a 7. 10) A bag contains 3 red marbles, 4 blue marbles, and 6 green marbles. A randomly drawn marble is blue. Use the given table to find the probability of the indicated event. Round your answer to the nearest thousandth. 11) College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results. toppings freshman sophomore junior senior cheese meat veggie A randomly selected student prefers a cheese topping. 12) One card is selected from a deck of cards. Find the probability of selecting a black card or a jack. Suppose P(C) =.048, P(M C) =.044, and P(M C) =.524. Find the indicated probability. 13) P(M') 14) Below is a table of data from a survey given to 1600 teenagers asking them to estimate what percentage of their classmates are using drugs. Find the probability that a randomly selected girl thinks that 50% or more of her classmates are using drugs. Round your answer to the nearest hundredth. None 1% - 24% 25% - 49% 50% - 74% 75% or more Boys Girls ) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd. 2

3 16) If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is a spade, given that the first card was a spade. 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 of the indicated result. 17) The second marble is red, given that the first marble is white. Find the probability. 18) In a certain city, 13% of the people are business executives, and 22% of the business executives drive Cadillacs. Assuming independent events, what is the probability of choosing a business executive who drives a Cadillac? Round the answer to the nearest hundredth. Solve the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary. 19) For two events M and N, P(M) =.2, P(N M) =.9, and P(N M') =.6. Find P(M N). Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the probability. 20) Two balls are drawn from a bag in which there are 4 red balls and 2 blue balls. The number of blue balls is counted. 21) Suppose you buy 1 ticket for $1 out of a lottery of 1000 tickets where the prize for the one winning ticket is to be $500. What are your expected winnings? 22) If 5 apples in a barrel of 25 apples are rotten, what is the expected number of rotten apples in a sample of 2 apples? Evaluate the expression. 23) 10 P 4 24) 7 C 4 Use the multiplication principle to solve the problem. 25) License plates are made using 3 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is allowed? 26) How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from? 27) There are 10 members on a board of directors. If they must form a subcommittee of 6 members, how many different subcommittees are possible? 28) A bag contains 3 blue, 4 red, and 4 green marbles. Four marbles are drawn at random from the bag. How many different samples are possible which include exactly two red marbles? 29) How many distinguishable permutations of letters are possible using the letters in the word COMMITTEE? 3

4 A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability. 30) One of each flavor A die is rolled five times and the number of fours that come up is tallied. Find the probability of getting the given result. 31) Exactly one four Find the probability of the event. 32) The probability that a radish seed will germinate is.7. The gardener plants 20 seeds and she harvests 16 radishes. Decide whether or not the matrix is a transition matrix. 33) Find the equilibrium vector for the transition matrix. 34) Find the requested long-range probabilities based on the transition matrix or data given. 35) Weather is classified as sunny or cloudy in a certain place. The probability that it will be sunny on a given day depends on whether it was sunny the previous day. The transition matrix is given below. Find the long-range prediction for the proportion of sunny and cloudy days. Sunny Cloudy Sunny Cloudy

5 Answer Key Testname: MATH 1324 T3RS14 1) 2) 32 3) {r, t, u, v, w, x, z} 4) {c, h, n, p, w} 5) 6) 14 7) 120 8) {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3)} 2 9) 13 10) ) ) ) ).22 15) 0 16) ) ).03 19).27 20) x P ) -$.50 22).4 23) ) 35 25) 17,576,000 26) 20,160 27) ) ) 45,360 30) ).402 5

6 Answer Key Testname: MATH 1324 T3RS14 32) ) No 34) [ ] 35) [ ] 6