Find the indicated probability. 1) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd.

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1 Math 0 Practice Test 3 Fall 2009 Covers 7.5, MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the indicated probability. ) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd. ) A) B) 2 C) 0 D) 6 2) If two fair dice are rolled, find the probability of a sum of 5 given that the sum is less than 8. A) 4 2 B) C) D) ) 3) You roll two fair dice. Let E be the event that the sum is even. Let F be the event that a four shows on at least one of the dice. Find P(F E). A) B) C) 7 5 D) ) 4) A box contains 24 blue marbles, 3 green marbles, and 3 red marbles. Two marbles are selected at random without replacement. Let E be the event that the first marble selected is green. Let F be the event that the second marble selected is green. Find P(F E). A) 3 49 B) 3 50 C) 2 49 D) ) 5) Two marbles are drawn without replacement from a box with blue, 3 white, 2 green, and 2 red marbles. Find the probability that the second marble is red, given that the first marble is white. 3 3 A) B) C) D) ) 6) Suppose one card is selected at random from an ordinary deck of 52 playing cards. Find the probability that the card is a diamond given that it is not a club. 6) A) 3 B) 4 C) D) 0 7) If three cards are drawn without replacement from an ordinary deck, find the probability that the third card is a heart, given that the first two cards were hearts. A) B) 6 C) D) ) Find the probability. 8) Assuming that boy and girl babies are equally likely, find the probability that a family with three children has all boys given that the first two are boys. 8) A) 8 B) 2 C) D) 4

2 9) A family has five children. The probability of having a girl is /2. What is the probability of having 2 girls followed by 3 boys? Round your answer to four decimal places. A) B) C) D) ) 0) Find the probability of correctly answering the first 3 questions on a multiple choice test if random guesses are made and each question has 5 possible answers. A) B) C) 5 D) ) Find the indicated probability. ) Assume that two marbles are drawn without replacement from a box with blue, 3 white, 2 green, and 2 red marbles. Find the probability that both marbles are green. A) 6 B) 4 C) 28 D) 4 ) Solve the problem. 2) 57% of a store's computers come from factory A and the remainder come from factory B. % of computers from factory A are defective while 4% 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? A) B) 0.07 C) 0.47 D) ) 3) 43% of a store's computers come from factory A and the remainder come from factory B. 5% of computers from factory A are defective while % 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 not defective and from factory A? A) 0.95 B) C) D) ) 4) In a certain U.S. city, 5.2% of adults are women. In that city, 4.6% of women and 0.9% of men suffer from depression. If an adult is selected at random from the city, find the probability that the person is a man who does not suffer from depression. A) B) C) 0.89 D) ) 5) In a certain U.S. city, 5.5% of adults are women. In that city, 3.4% of women and 9.6% of men suffer from depression. If an adult is selected at random from the city, find the probability that the person suffers from depression. A) 0.34 B) C) 0.6 D) 0.5 5) 2

3 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. 6) Toppings Freshman Sophomore Junior Senior Totals Cheese Meat Veggie A student is selected at random. Find the probability that the student's favorite topping is meat given that the student is a junior. A) B) C) D) ) College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results. 7) Toppings Freshman Sophomore Junior Senior Totals Cheese Meat Veggie A student is selected at random. Find the probability that the student's favorite topping is veggie given that the student is a junior or senior. A) 0.45 B) 0.64 C) D) ) People in a survey were given three choices of soft drinks and asked to choose one favorite. The following table shows the results. 8) cola root beer lemon-lime totals under 2 years of age between 2 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. A) C) B) 4 7 D) none of the above 3

4 9) People in a survey were given three choices of soft drinks and asked to choose one favorite. The following table shows the results. 9) cola root beer lemon-lime totals under 2 years of age between 2 and over 40 years of age One of the participants is selected at random. Find the probability that the person is over 40 given that they prefer root beer. A) B) C) D) Evaluate the factorial. 20) 6! A) 20 B) 360 C) 440 D) ) Evaluate the permutation. 2) P(0, 5) A) 720 B) 0 C) 30,240 D) 2) 22) P(25, 5) A) 303,600 B) C) 27,52,000 D) 6,375,600 22) Solve the problem. 23) Suppose there are 6 roads connecting town A to town B and 4 roads connecting town B to town C. In how many ways can a person travel from A to C via B? A) 0 ways B) 36 ways C) 24 ways D) 6 ways 23) 24) In how many ways can 4 people be chosen and arranged in a straight line, if there are 6 people from whom to choose? A) 24 ways B) 360 ways C) 30 ways D) 60 ways 24) 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? A),757,600 plates B),000,000 plates C) 308,95,776 plates D) 7,576,000 plates 25) 26) A person ordering a certain model of car can choose any of 9 colors, either manual or automatic transmission, and any of 9 audio systems. How many ways are there to order this model of car? A) 62 ways B) 70 ways C) 72 ways D) 58 ways 26) 27) A shirt company has 4 designs that can be made with short or long sleeves. There are 6 color patterns available. How many different types of shirts are available from this company? A) 2 types B) 24 types C) 0 types D) 48 types 27) 28) A restaurant offers 7 possible appetizers, 3 possible main courses, and 6 possible desserts. How many different meals are possible at this restaurant? (Two meals are considered different unless all three courses are the same). A) 546 meals B) 26 meals C) 536 meals D) 343 meals 28) 4

5 How many distinguishable permutations of letters are possible in the word? 29) GIGGLE A) 20 B) 4320 C) 36 D) ) 30) TENNESSEE A) 8 B) 362,880 C) 7560 D) ) 3) COLORADO A) 3,440 B) 6720 C) 4480 D) 40,320 3) Four accounting majors, two economics majors, and three marketing majors have interviewed for five different positions with a large company. Find the number of different ways that five of these could be hired. 32) There is no restriction on the college majors hired for the five positions. 32) A) 24 ways B) 3024 ways C) 5,20 ways D) 20 ways 33) Two accounting majors must be hired first, then one economics major, then two marketing majors. A) 288 ways B) 4 ways C) 44 ways D) 24 ways 33) 34) One accounting major, one economics major, and one marketing major would be hired, then the two remaining positions would be filled by any of the majors left. A) 48 ways B) 4320 ways C) 720 ways D) 260 ways 34) Evaluate the combination ) A) 2 B) 24 C) 24! - 0 D) 24! 35) 36) 7 0 A) 2520 B) 260 C) D) ) 37) 9 A) 9! - 0 B) 9 C) 9! D) 2 37) 38) 3 3 A) 3! - 5 B) C) 2 D) 3! 38) Of the 2,598,960 different five -card hands possible from a deck of 52 playing cards, how many would contain the following cards? 39) No face cards 39) A) 639,730 hands B) 658,008 hands C) 39,865 hands D) 27,946 hands 40) All hearts A) 287 hands B) 43 hands C) 386 hands D) 2574 hands 40) 5

6 4) Two black cards and three red cards A),690,000 hands B),267,500 hands C) 845,000 hands D) 422,500 hands 4) Solve the problem. 42) If you toss five fair coins, in how many ways can you obtain at least one head? A) 6 ways B) 32 ways C) 3 ways D) 5 ways 42) 43) If you toss six fair coins, in how many ways can you obtain at least two heads? A) 58 ways B) 57 ways C) 64 ways D) 63 ways 43) 44) A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without looking, how many ways can you get 5 apples? A) 24 ways B) 0 ways C) 6 ways D) 2 ways 44) 45) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how many ways can you get 4 oranges? A) 5 ways B) 5 ways C) 8 ways D) 0 ways 45) Decide whether the situation involves permutations or combinations. 46) A batting order for 9 players for a baseball game. A) Permutation B) Combination 46) 47) A selection of a chairman and a secretary from a committee of 5 people. A) Permutation B) Combination 47) 48) A sample of 0 items taken from 90 items on an assembly line. A) Permutation B) Combination 48) Solve the problem. 49) How many three-digit counting numbers do not contain any of the digits, 5, 7, 8, or 9? A) 00 numbers B) 25 numbers C) 48 numbers D) 64 numbers 49) 50) In how many ways can a group of 6 students be selected from 7 students? A) way B) 6 ways C) 7 ways D) 42 ways 50) 5) How many ways can a committee of 2 be selected from a club with 2 members? A) 2 ways B) 32 ways C) 33 ways D) 66 ways 5) 52) In how many ways can a group of 7 students be selected from 8 students? A) way B) 8 ways C) 56 ways D) 7 ways 52) 53) If the police have 8 suspects, how many different ways can they select 5 for a lineup? A) 336 ways B) 6720 ways C) 56 ways D) 40 ways 53) 54) The chorus has six sopranos and eight baritones. In how many ways can the director choose a quartet that contains at least one soprano? A) 07 ways B) 986 ways C) 00 ways D) 93 ways 54) 6

7 55) A class has 0 boys and 2 girls. In how many ways can a committee of four be selected if the committee can have at most two girls? A) 4620 ways B) 5665 ways C) 570 ways D) 440 ways 55) 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. 56) All lemon 56) A) B) 0.22 C) 0.06 D) 0 57) All orange A) B) C) D) ) 58) 2 cherry, lemon A) B) C) 0.22 D) ) 59) cherry, 2 lemon A) B) C) D) ) Find the probability of the following card hands from a 52 -card deck. In poker, aces are either high or low. A bridge hand is made up of 3 cards. 60) In bridge, 6 of one suit, 4 of another, and 3 of another 60) A) B) C) D) ) In bridge, all cards in one suit A) B) C) D) ) In bridge, 4 aces A) B) C) D) ) 62) 63) In bridge, exactly 3 kings and exactly 3 queens A) B) C) D) ) Solve. 64) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 0? A) 8 B) 5 8 C) 3 D) 2 64) 65) In a state lotto you have to pick 4 numbers from to 45. If your numbers match those that the state draws, you win. If you buy 3 tickets, what is your probability of winning? 8 A) B) C) D) ) 66) A lottery game contains 29 balls numbered through 29. What is the probability of choosing a ball numbered 30? A) 29 B) C) 0 D) 29 66) 7

8 Solve the problem. 67) What is the probability that at least 2 of the 435 members of the House of Representatives have the same birthday? A) B) C) D) 67) 68) At the first tri-city meeting, there were 8 people from town A, 7 people from town B, and 5 people from town C. If the council consists of 5 people, find the probability of 3 from town A and 2 from town B. A) B) C) D) ) 69) At the first tri-city meeting, there were 8 people from town A, 7 people from town B, and 5 people from town C. If the council consists of 5 people, find the probability of 2 from town A, 2 from town B, and from town C. A) B) 0.89 C) D) ) 70) A roulette wheel contains 84 slots numbered through 84. The slots,4,7,... are red, the slots 2,5,8,... are green, and the slots 3, 6, 9,... are brown. When the wheel is spun, a ball rolls around the rim and falls into a slot. What is the probability that the ball falls into a green slot? 70) A) 3 B) 2 5 C) 4 D) 2 3 8

9 Answer Key Testname: MATH0 PRACTICETEST3FALL2009 ) C 2) B 3) D 4) C 5) D 6) A 7) A 8) B 9) D 0) A ) C 2) B 3) C 4) D 5) C 6) C 7) C 8) C 9) A 20) D 2) C 22) D 23) C 24) B 25) D 26) A 27) D 28) A 29) A 30) D 3) B 32) C 33) C 34) C 35) B 36) C 37) B 38) B 39) B 40) A 4) C 42) C 43) B 44) C 45) D 46) A 47) A 48) B 49) A 50) C 9

10 Answer Key Testname: MATH0 PRACTICETEST3FALL2009 5) D 52) B 53) C 54) D 55) A 56) D 57) B 58) D 59) C 60) B 6) C 62) C 63) A 64) D 65) D 66) C 67) D 68) A 69) B 70) A 0

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