MATH CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #1 - SPRING DR. DAVID BRIDGE

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1 MATH CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #1 - SPRING 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. 1) 10 {20, 0, 0, 50, 60} 2) {2, 6, 15} = {0, 2, 6, 15} ) {55, 56, 55, 56} = {55, 56} 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. ) {, 6, 8} {,, 5, 6, 8} 5) {17, 1, 6} {18, 1, 6, 6} 6) {9, 11, } {x x is an odd counting number} 7) {a, d, j} {a, d, j} Find the number of subsets of the set. 8) {8, 9, 10} ) {0} ) {mom, dad, son, daughter} TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Decide whether the statement is true or false. 11) {5, 10, 15, 20} {5, 15} = {5, 10, 15, 20} 12) {7, 1, 21, 28} {7, 21} = {7, 1, 21, 28} ) {8, 5, 15} = {8, 5, 15} 1) {7, 5, 15} = {7, 5, 15}

2 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. 15) A B' {u, w} {t, v, x} {q, s, t, u, v, w, x, y} {r, s, t, u, v, w, x, z} 16) (A ' {r, s, t, u, v, w, x, z} {r, t, v, x} {t, v, x} {s, u, w} 17) (A ' {q, s, t, u, v, w, x, y} {s, u, w} {t, v, x} {r, t, u, v, w, x, z} 18) A' B {r, s, t, u, v, w, x, z} {q, r, s, t, v, x, y, z} {q, s, t, u, v, w, x, y} {s, u, w} 19) A (B {q, r, w, y, z} {q, w, y} {q, s, u, w, y, z} {q, y, z} 20) B (A {q, s, u, w, y, z} {q, r, w, y, z} {q, s, y, z} {q, w, y} Shade the Venn diagram to represent the set. 21) A' B' 22) A' B' 2) (A B C')'

3 2) (A B C')' 25) (A' C Use the union rule to answer the question. 26) If n( =, n( = 9, and n(a = 2; what is n(a? ) If n( = 8, n( = 21, and n(a = 25; what is n(a? ) If n( = 8, n(a = 9, and n(a = 8; what is n(? ) If n( = 20, n(a = 58, and n(a = 16; what is n(? Use a Venn Diagram and the given information to determine the number of elements in the indicated set. 0) n(u) = 60, n( = 0, n( = 2, and n(a = 2. Find n(a '

4 1) n( = 65, n( = 7, n( = 67, n(a =, n(a = 15, n(b = 9, n(a B = 7, and n(a' B' C') = 1. Find n(u) ) n(a B = 17, n(a B = 2, n(a = 8, n(a = 5, n(b =, n( = 116, n( = 86, and n( = 8. Find n(a' B ) n(u) = 87, n( =, n( = 7, n( = 1, n(a = 10, n(a = 7, n(b = 7, and n(a B = 5. Find n((a B ') Use a Venn diagram to answer the question. ) At the University of Edmond (EU) there are 685 students taking College Algebra or Calculus & Statistics. 95 are taking College Algebra, 20 are taking Calculus & Statistic, and 0 are taking both College Algebra and Calculus & Statistic. How many are taking Calculus & Statistic but not College Algebra? ) 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 150 responses with the following results: 5 were interested in an interview show and a documentary, but not reruns; 6 were interested in an interview show and reruns, but not a documentary; 21 were interested in reruns but not an interview show; 6 were interested in an interview show but not a documentary; 15 were interested in a documentary and reruns; 9 were interested in an interview show and reruns; 12 were interested in none of the three. How many are interested in exactly one kind of show? ) A survey of a group of 1 tourists was taken in St. Louis. The survey showed the following: 62 of the tourists plan to visit Gateway Arch; 6 plan to visit the zoo; 9 plan to visit the Art Museum and the zoo, but not the Gateway Arch; 1 plan to visit the Art Museum and the Gateway Arch, but not the zoo; 17 plan to visit the Gateway Arch and the zoo, but not the Art Museum; 7 plan to visit the Art Museum, the zoo, and the Gateway Arch; 16 plan to visit none of the three places. How many plan to visit the Art Museum only? Find the probability of the given event. 7) A card drawn from a well-shuffled deck of cards is a red ace ) A card drawn from a well-shuffled deck of cards is red

5 9) A card drawn from a well-shuffled deck of cards is an ace or a ) A card drawn from a well-shuffled deck of cards is a face card or a ) A bag contains 5 red marbles, 8 blue marbles, and 9 green marbles. A randomly drawn marble is blue ) A bag contains 7 red marbles, blue marbles, and 1 green marble. A randomly drawn marble is not blue Use the given table to find the probability of the indicated event. Round your answer to the nearest thousandth. ) 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 ) 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 meat topping Determine whether the given events are disjoint. 5) Knowing Spanish and knowing Chinese Yes No 6) Drawing a face card from a deck of cards and drawing a deuce No Yes 7) Being a teenager and being President of the United States No Yes

6 Solve the problem. 8) A single die is rolled one time. Find the probability of rolling an odd number or a number less than ) One card is selected from a deck of cards. Find the probability of selecting a black card or a jack ) One card is selected from a deck of cards. Find the probability of selecting a red card or a heart ) One card is selected from a deck of cards. Find the probability of selecting a diamond or a card less than 10. (Note: The ace is considered a low card.) Suppose P( =.08, P(M =.0, and P(M =.. Find the indicated probability. ) P[(M '] ) P(M' C') ) P(M' C') ) P[(M '] 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. 56) Outcomes Probabilities a.1 b. c.2 d. No Yes 57) Outcomes Probabilities a.1 b.26 c.20 d.2 Yes No

7 58) Outcomes Probabilities a.50 b. c.11 d.16 Yes No 59) Outcomes Probabilities a 5/16 b 5/8 c 1/8 d -1/16 No Yes Solve the problem. 60) A survey revealed that 7% of people are entertained by reading books, 5% are entertained by watching TV, and 8% 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. 100% 92% 8% 8% 61) Of the coffee makers sold in an appliance store,.0% have either a faulty switch or a defective cord, 2.% have a faulty switch, and 0.5% have both defects. What is the probability that a coffee maker will have a defective cord? Express the answer as a percentage..0% 2.1%.5% 2.9% 62) If a single fair die is rolled, find the probability of a given that the number rolled is odd ) If a single fair die is rolled, find the probability of a 5 given that the number rolled is odd ) If two fair dice are rolled, find the probability of a sum of 6 given that the roll is a double ) If two fair dice are rolled, find the probability that the roll is a double given that the sum is ) 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

8 67) 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 ) 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 ) If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is an ace, given that the first card was an ace Assume that two marbles are drawn without replacement from a box with 1 blue, white, 2 green, and 2 red marbles. Find the probability of the indicated result. 70) The second marble is red, given that the first marble is white ) The second marble is white, given that the first marble is blue Use the given table to find the indicated probability. 72) 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 P(favorite topping is meat student is junior)? Round the answer to the nearest hundredth ) 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 P(favorite topping is veggie student is junior or senior)? Round the answer to the nearest hundredth

9 7) The following table contains data from a study of two airlines which fly to Smalltown, USA. Number of flights arrived on time Number of flights arrived late Podunk Airlines 6 Upstate Airlines 5 P(flight arrived on time flight was on Upstate Airlines)? None of the above 75) The following table contains data from a study of two airlines which fly to Smalltown, USA. Number of flights arrived on time Number of flights arrived late Podunk Airlines 6 Upstate Airlines 5 P(flight was on Upstate Airlines flight arrived late)? None of the above

10 Answer Key Testname: MATH PRACTICE EXAM #1 1) FALSE 2) FALSE ) TRUE ) B 5) A 6) B 7) B 8) A 9) D 10) D 11) FALSE 12) TRUE ) TRUE 1) FALSE 15) A 16) B 17) D 18) B 19) C 20) C 21) B 22) B 2) A 2) B 25) A 26) A 27) B 28) C 29) C 0) A 1) A 2) D ) D ) B 5) C 6) A 7) D 8) C 9) B 0) B 1) B 2) B ) A ) C 5) B 6) B 7) B 8) B 9) D 50) D 51) D ) C 5) D 5) B 55) C 56) B 57) A 58) B 59) A 60) D 61) B 62) D 6) B 6) C 65) B 66) C 67) B 68) D 69) C 70) C 71) C 72) D 7) A 7) C 75) B