Exam. Name. Find the number of subsets of the set. 1) {x x is an even number between 11 and 31} 2) {13, 0, 13, 14, 15}


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1 Exam Name Find the number of subsets of the set. 1) {x x is an even number between 11 and 31} 2) {13, 0, 13, 1, 15} Let A = 6,, 1, 3, 0, 8, 9. Determine whether the statement is true or false. 3) 9 A ) 3 A Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; D = {2, 5, 8}; and U = {1, 2, 3,, 5, 6, 7, 8}. Determine whether the given statement is true or false. 5) B D 6) {0} U Decide whether the statement is true or false. 7) {13, 10, 6} {6, 13, 10} = {13, 6} 8) {3, 2, 13} = {3, 2, 13} Insert " " or " " in the blank to make the statement true. 9) {0, 6} {, 6} 10) {b, g, d} {b, g, d} Find the cardinal number of the indicated set by referring to the given table. 11) 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. NonHispanic White (A) African Americ (C) Hispanic (B) Democrat (D) Republican (R) Other (O) Totals Find the number of people in the set D (B O) 12) 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. NonHispanic White (A) African Americ (C) Hispanic (B) Democrat (D) Republican (R) Other (O) Totals Find the number of people in the set R' (A F) 1
2 Shade the Venn diagram to represent the set. 13) (A B C')' 20) A card is drawn from a wellshuffled deck of 52 cards. What is the probability of drawing a face card or a 5? 21) When a single card is drawn from a wellshuffled 52card deck, find the probability of getting a red card. 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. Use a Venn diagram to answer the question. 1) A survey of 180 families showed that 67 had a dog; 52 had a cat; 22 had a dog and a cat; 70 had neither a cat nor a dog, and in addition did not have a parakeet; had a cat, a dog, and a parakeet. How many had a parakeet only? Use a Venn Diagram and the given information to determine the number of elements in the indicated region. 15) n(a) = 17, n(a B C) = 8, n(a C) = 12, n(a B') = 6, n(b C) = 15, n(b C') = 12, n(b C) = 32, n(a' B' C') = 10. Find n(a'). Find the probability of the given event. 16) A single fair die is rolled. The number on the die is prime. 17) Two fair dice are rolled. The sum of the numbers on the dice is 1 or 5. Find the probability. 18) Each digit from the number 6,727,887 is written on a different card. If one of these cards is selected at random, what is the probability of drawing a card that shows 6 or 8? 22) Find the odds. Outcomes Probabilities a 1/8 b 1/8 c 3/8 d 11/16 23) Find the odds in favor of rolling a number less than 3 when a fair die is rolled. 2) Find the odds in favor of drawing an even number when a card is drawn at random from the cards shown below. 25) Find the odds against correctly guessing the answer to a multiple choice question with 7 possible answers. Solve the problem. 26) The odds in favor of Jerome beating his friend in a round of golf are 1 :. Find the probability that Jerome will beat his friend. 27) The odds against Carl beating his friend in a round of golf are 9 : 2. Find the probability that Carl will lose. Find the indicated probability. 19) Each digit from the number 8,33,993 is written on a different card. If one of these cards is selected at random, what is the probability of drawing a card that shows 8, 3, or? 28) If you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade? 29) Find the probability that the sum is either 10 or at most 3 when two fair dice are rolled. 2
3 Solve the problem. 30) Of the coffee makers sold in an appliance store, 5.0% have either a faulty switch or a defective cord, 1.8% 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. 31) Among 170 households surveyed, 58 have a video camera, 5 have a snapshot camera, 23 have binoculars, have a video camera and a snapshot camera, 9 have a snapshot camera and binoculars, and 3 have all three products. What is the probability that a household will have a snapshot camera or binoculars? Express the answer as a fraction. Find the indicated probability. 32) Suppose one card is selected at random from an ordinary deck of 52 playing cards. Let A = event a queen is selected B = event a diamond is selected. Determine P(B A). 33) 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. 3) 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. 35) If a single fair die is rolled, find the probability of a given that the number rolled is odd. 36) If two fair dice are rolled, find the probability that the roll is a double given that the sum is ) Assume that two marbles are drawn without that the second marble is white, given that the first marble is blue. Use the given table to find the indicated probability. 38) The following table contains data from a study of two airlines which fly to Smalltown, USA. Number of flights arrived on time Number o arrived la Podunk Airlines 33 6 Upstate Airlines 3 5 If a flight is selected at random, what is the probability that it was on Upstate Airlines given that it arrived late? Find the probability. 39) If 80% of scheduled flights actually take place and cancellations are independent events, what is the probability that 3 separate flights will all take place? 0) A basketball player hits her shot 5% of the time. If she takes four shots during a game, what is the probability that she misses the first shot and hits the last three? Express the answer as a percentage, and round to the nearest tenth (if necessary). Assume independence of shots. Solve the problem. 1) The probability that a person passes a test on the first try is The probability that a person who fails the first test will pass on the second try is The probability that a person who fails the first and second tests will pass the third time is 0.6. Find the probability that a person fails the first and second tests and passes on the third try. 2) 52% of a store's computers come from factory A and the remainder come from factory B. 2% of computers from factory A are defective while 3% of computers from factory B are defective. If one of the store's computers is selected at random, what is the probability that it is defective and from factory B? 3
4 Find the indicated probability. 3) Assume that two marbles are drawn without that the first marble is white and the second marble is blue. ) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a king and the second card is a queen. 9) A company is conducting a sweepstakes, and ships two boxes of game pieces to a particular store. Box A has 5% of its contents being winners, while % of the contents of box B are winners. Box A contains 0% of the total tickets. The contents of both boxes are mixed in a drawer and a ticket is chosen at random. What is the probability it came from box A if it is a winner? 5) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. 6) Assume that two marbles are drawn without that one marble is green, and one marble is red. Use Bayes' rule to find the indicated probability. 7) 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? 8) In one town, 8% of year olds own a house, as do 2% of year olds and 5% of those over 50. According to a recent census taken in the town, 27.0% of adults in the town are years old, 36.5% are years old, and 36.5% are over 50. What percentage of houseowners are years old?
5 Answer Key Testname: 132SETPT 1) 102 2) 32 3) TRUE ) FALSE 5) TRUE 6) FALSE 7) FALSE 8) FALSE 9) 10) 11) 61 12) ) 29) ) 3.7% 31) ) ) ) ) 0 36) 0 37) 3 7 1) 13 15) 27 16) ) ) ) ) 13 38) ).51 0) 5% 1) ) ) 56 ) 5) 6) ) ) ) ) ) No; the sum of the probabilities is not 1 23) 1 to 2 2) 2 to 3 25) 6 : 1 26) ) )
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