MATH 205 - CALCULUS & STATISTICS/BUSN - PRACTICE EXAM # - SPRING 2006 - DR. DAVID BRIDGE TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Tell whether the statement is true or false. ) 7 {4, 2, 28, 5, 42} 2) {57, 58, 57, 58} = {57, 58} MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Insert " " or " " in the blank to make the statement true. ) {5, 7, 9} {4, 5, 6, 7, 9} 4) {5, 22, 27} {2, 22, 27, 7} 5) {x x is a counting number larger than 5} {7, 8, 9,... } Find the number of subsets of the set. 6) {2,, 4} 8 7 6 D) 7) {mom, dad, son, daughter} 4 6 8 D) 2 TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Decide whether the statement is true or false. 8) {7, 4, 2, 28} {7, 2} = {7, 4, 2, 28} 9) {9, 8, 27, 6} {9, 27} = {9, 8, 27, 6} 0) {5,, 0} = {5,, 0} ) {, 5, 7} {4, 6, 8} = {, 5, 7, 4, 6, 8} MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 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. 2) A B' {r, s, t, u, v, w, x, z} {u, w} {q, s, t, u, v, w, x, y} D) {t, v, x}
) (A ' {t, v, x} {s, u, w} {r, t, v, x} D) {r, s, t, u, v, w, x, z} 4) (A ' {r, t, u, v, w, x, z} {s, u, w} {q, s, t, u, v, w, x, y} D) {t, v, x} Shade the Venn diagram to represent the set. 5) A' B' 6) A' B' D)
7) (A (A ' 8) (A B C')'
9) C' (A Use the union rule to answer the question. 20) If n( = 5, n( =, and n(a = ; what is n(a? 4 6 D) 2 2) If n( = 2, n( = 9, and n(a = 09; what is n(a? 6 48 8 D) 8 Use a Venn Diagram and the given information to determine the number of elements in the indicated set. 22) n(u) = 60, n( = 5, n( = 24, and n(a = 4. Find n(a '. 55 59 D) 5
2) n( = 65, n( = 7, n( = 67, n(a =, n(a = 5, n(b = 9, n(a B = 7, and n(a' B' C') =. Find n(u). 6 75 06 D) 240 TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Use a Venn diagram to decide if the statement is true or false. 24) A B' = (A' ' 25) (A' ' = A' B MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a Venn diagram to answer the question. 26) At UCO there are 765 students taking College Algebra or Calculus. 405 are taking College Algebra, 407 are taking Calculus, and 47 are taking both College Algebra and Calculus. How many are taking Algebra but not Calculus? 78 58 D) 60 Write the sample space for the given experiment. 27) An ordinary die is rolled. {, 2,, 4, 5, 6} {, 6} {6} D) {6}
For the experiment described, write the indicated event in set notation. 28) A die is tossed twice with the tosses recorded as an ordered pair. Represent the following event as a subset of the sample space: The first toss shows a five. {(5, ), (5, 2), (5, ), (5, 4), (5, 5), (5, 6)} {(5, ), (5, 2), (5, 4), (5, 5), (5, 6)} {(5, )} D) {(5, ), (5, ), (5, 5)} 29) A coin is tossed three times. Represent the event "the first toss comes up tails" as a subset of the sample space. {thh, tht, tth} {tails, heads, heads} {thh, tht, tth, ttt} D) {hhh, hht, hth, htt, thh, tht, tth, ttt} A die is rolled twice. Write the indicated event in set notation. 0) The sum of the rolls is. {(6, 7)} {(7, 6)} D) {(6, 7), (7, 6)} Find the probability of the given event. ) A card drawn from a well-shuffled deck of 52 cards is a red ace. 52 26 D) 2 2) A card drawn from a well-shuffled deck of 52 cards is a face card or a 6. 2 6 2 D) 4 ) A bag contains 4 red marbles, blue marbles, and 5 green marbles. A randomly drawn marble is blue. 5 D) 4 7 2 4) A bag contains 6 red marbles, blue marbles, and green marble. A randomly drawn marble is not blue. 7 0 D) 7 0 0 7 Use the given table to find the probability of the indicated event. Round your answer to the nearest thousandth. 5) 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 28 25 meat 8 25 veggie 8 25 A randomly selected student prefers a cheese topping. 0.65 0.25 0.8 D) 0.8
Determine whether the given events are mutually exclusive. 6) Knowing Spanish and knowing Chinese No Yes 7) Drawing a spade from a deck of cards and drawing an ace No Yes 8) Drawing a face card from a deck of cards and drawing a 6 No Yes Solve the problem. 9) A single die is rolled one time. Find the probability of rolling an odd number or a number less than 5. 2 2 D) 5 6 40) A single die is rolled one time. Find the probability of rolling a number greater than or less than 4. 4 6 D) 4) One card is selected from a deck of cards. Find the probability of selecting a red card or a jack. 27 7 D) 5 52 26 26 42) One card is selected from a deck of cards. Find the probability of selecting a red card or a diamond. 4 2 4 D) 0 Suppose P( =.048, P(M =.044, and P(M =.524. Find the indicated probability. 4) P(M) 0.528 0.520 0.472 D) 0.480 44) P(C') 0.956 0.476 0.952 D).000 45) P(M' C') 0.568 0.476 0.564 D) 0.956
Solve the problem. 46) A survey revealed that 49% of people are entertained by reading books, 47% are entertained by watching TV, and 4% are entertained by both books and TV. What is the probability that a person will be entertained by either books or TV? Express the answer as a percentage. 00% 96% 92% D) 4% 47) Of the coffee makers sold in an appliance store, 4.0% have either a faulty switch or a defective cord, 2.2% have a faulty switch, and 0.7% have both defects. What is the probability that a coffee maker will have a defective cord? Express the answer as a percentage. 4.7% 4.0% 2.9% D) 2.5% 48) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd. 6 0 D) 2 49) If a single fair die is rolled, find the probability of a 5 given that the number rolled is odd. 2 2 D) 6 50) If two fair dice are rolled, find the probability of a sum of 6 given that the roll is a double. 6 5 4 D) 5) 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. 4 D) 7 5 2
52) If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is red, given that the first card was a heart. 22 26 25 4 D) 2 5 5 7 5) If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is a face card, given that the first card was a queen. 5 4 D) 7 5 7 Assume that two marbles are drawn without replacement from a box with blue, white, 2 green, and 2 red marbles. Find the probability of the indicated result. 54) The second marble is white, given that the first marble is blue. 7 56 64 D) 8 55) The second marble is blue, given that the first marble is blue. 0 8 28 D) 7 56) Both marbles are red. 28 6 56 D) 4 57) One marble is white, and one marble is blue. 4 28 56 D) 2 Find the probability. 58) If 8% of scheduled flights actually take place and cancellations are independent events, what is the probability that separate flights will take place? 0.8 0.5 0.0 D) 0.66 59) A calculator requires a keystroke assembly and a logic circuit. Assume that 88% of the keystroke assemblies and 76% of the logic circuits are satisfactory. Find the probability that a finished calculator will be satisfactory. 0.6688 0.5776 0.8200 D) 0.7744 60) 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. D) 69 204 204 6
Use the given table to find the indicated probability. 6) 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 2 26 2 meat 28 2 2 veggie 2 28 2 P(favorite topping is meat student is junior)? Round the answer to the nearest hundredth. 0.54 0.94 0.76 D) 0.059 62) People were given three choices of soft drinks and asked to choose one favorite. The following table shows the results. cola root beer lemon-lime under 2 years of age 40 25 20 between 2 and 40 5 20 0 over 40 years of age 20 0 5 P(person drinks root beer person is over 40)? 6 2 7 7 2 5 D) None of the above Solve the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary. 6) For two events M and N, P(M) =.5, P(N M) =.7, and P(N M') =.8. Find P(M N)..47.0 0 D).5 64) For mutually exclusive events X, X2, and X, let P(X) =.47, P(X2) =.2, and P(X) =.2. Also, P(Y X) =.40, P(Y X2) =.0, and P(Y X) =.60. Find P(X2 Y)..2.47.46 D). Solve the problem. Express the answer as a percentage. 65) At the University of Edmond, 60% of all students are classified as lower-division, and 40% are classified as upper-division. Among the lower-division students, 0% will buy a new car, and among the upper-division students, 80% will buy a new car. A student is seen buying a new car. What is the probability that (s)he is a lower-division student? 64% 70% 6% D) 20% Evaluate the expression. 66) 0!,628,790 62,880,628,80 D),628,800
67) 0P 20 27 720 D) 7 68) 0 5040 20 5,20 D) 69) 2 0 2 9,96,800 D) Use the multiplication principle to solve the problem. 70) How many ways can one arrange the letters A, B, C, D? 4 8 24 D) 64 7) José has 5 shirts in his closet. He must pick a different shirt to wear on each day of the school week (Monday through Friday). In how many ways can he do this? 625 5 25 D) 20 Solve the problem. 72) How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from? 40,20 48 720 D) 20,60 7) There are members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible? 990 65 D) 9,96,800 74) There are 0 members on a board of directors. If they must form a subcommittee of 6 members, how many different subcommittees are possible? 720 5,200 20 D),000,000 75) Five cards are drawn at random from an ordinary deck of 52 cards. In how many ways is it possible to draw all red cards? 26,20 ways 65,780 ways,560 ways D) 2,890 ways
Answer Key Testname: MATH 205 PRACTICE EXAM ) FALSE 2) TRUE ) B 4) B 5) A 6) A 7) B 8) FALSE 9) TRUE 0) TRUE ) FALSE 2) B ) C 4) A 5) B 6) D 7) A 8) B 9) B 20) B 2) A 22) D 2) C 24) TRUE 25) FALSE 26) C 27) A 28) A 29) C 0) B ) B 2) D ) A 4) B 5) A 6) A 7) A 8) B 9) D 40) D 4) B 42) B 4) B 44) C 45) B 46) C 47) D 48) C 49) B 50) A 5) A 52) C
Answer Key Testname: MATH 205 PRACTICE EXAM 5) C 54) A 55) A 56) A 57) B 58) B 59) A 60) D 6) B 62) A 6) A 64) A 65) C 66) D 67) C 68) B 69) D 70) C 7) D 72) D 7) A 74) C 75) B