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 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary. 1) For two events M and N, P(M) =.2, P(N M) =.5, and P(N M') =.9. Find P(M N) ) For two events M and N, P(M) =.8, P(N M) =.5, and P(N M') =.3. Find P(M' N) ) For mutually exclusive events X 1, X 2, and X 3, let P(X 1 ) =.24, P(X 2 ) =.23, and P(X 3 ) =.53. Also, P(Y X 1 ) =.40, P(Y X 2 ) =.30, and P(Y X 3 ) =.60. Find P(X 1 Y) ) For mutually exclusive events X 1, X 2, and X 3, let P(X 1 ) =.20, P(X 2 ) =.56, and P(X 3 ) =.24. Also, P(Y X 1 ) =.40, P(Y X 2 ) =.30, and P(Y X 3 ) =.60. Find P(X 2 Y) Solve the problem. Express the answer as a percentage. 5) 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, 30% 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? 36% 70% 20% 64% 6) At the University of Edmond, 45% of all students are classified as lower-division, 35% are classified as upper-division, and 20% are graduate students. Among the lower-division students, 60% were born in Oklahoma, among the upper-division students, 40% were born in Oklahoma, and among the graduate students, 30% were born in Oklahoma. A randomly selected student was born in Oklahoma. What is the probability the (s)he is a graduate student? 26% 57% 13% 30% The table shows, for some particular year, a listing of several income levels and, for each level, the proportion of the population in the level and the probability that a person in that level bought a new car during the year. Given that one of the people who bought a new car during that year is randomly selected, find the probability that that person was in the indicated income category. Round your answer to the nearest hundredth. Income level Proportion of population Probability that bought a new car $ %.02 $ %.03 $10,000-14, %.06 $15,000-19, %.07 $20,000-24, %.09 $25,000-29, %.10 $30,000-34, %.11 $35,000-39, %.13 $40,000-49, %.15 $50,000 and over 14.7%.19 7) $ $

2 8) $50,000 and over ) $30,000 - $39, Provide an appropriate response. 10) If P(A = 0.2, can P( = 0.9, P( = 0.7, are A and B be independent events? Yes No 11) If A and B are independent events, how many of the following statements must be true? (i) A' and B are independent. (ii) A and B' are independent. (iii) A' and B' are independent. All Two None One Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the probability. 12) Three coins are tossed, and the number of tails is noted. 0 1/3 1 1/6 2 1/6 3 1/3 0 1/6 1 1/3 2 1/3 3 1/6 0 3/16 1 5/16 2 5/16 3 3/16 0 1/8 1 3/8 2 3/8 3 1/8 13) Three cards are drawn from a deck. The number of kings is counted ) 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 ) Four cards are drawn from a deck. The number of red tens is counted Evaluate the expression. 16) 6!

3 17) 6 P ) 5 P ) 10 C , ) 11 C ,628, ) 39 C ) 19 C 8 75,582 75,607 75,554 75,597 Solve the problem. 23) How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetition of digits is not allowed? ) José has 7 shirts in his closed. He must select 4 shirts to wear at a 4-day conference. In how many different ways can he decide which shirt to wear each day, if he does not wear any shirt more than once? ) How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from? 40, ,160 26) A musician plans to perform 4 selections. In how many ways can she arrange the musical selections? ) There are 6 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? ) In how many ways can 5 letters be chosen from the set {A, B, C, D, E, F} if order is important and no repeats are allowed? ) There are 8 members on a board of directors. If they must form a subcommittee of 3 members, how many different subcommittees are possible? ) In a certain lottery, 6 numbers between 1 and 12 inclusive are drawn. These are the winning numbers. How many different selections are possible? Assume that the order in which the numbers are drawn is not important ,985, ,280

4 31) How many ways can an IRS auditor select 5 of 8 tax returns for an audit? 32, ) If the police have 8 suspects, how many different ways can they select 5 for a lineup? 56 ways 336 ways 6720 ways 40 ways 33) Five cards are drawn at random from an ordinary deck of 52 cards. In how many ways is it possible to draw two red cards and three black cards? 422,500 ways 1,690,000 ways 1,267,500 ways 845,000 ways 34) Five cards are drawn at random from an ordinary deck of 52 cards. In how many ways is it possible to draw two red aces and two black jacks? 1,152 ways 48 ways 192 ways 144 ways 35) A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the committee can have at most two girls? 5665 ways 4620 ways 5170 ways 4410 ways 36) A bag contains 5 blue, 4 red, and 3 green marbles. Four marbles are drawn at random from the bag. How many different samples are possible which include exactly two red marbles? 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. 37) All cherry ) All lemon ) 2 cherry, 1 lemon ) One of each flavor 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 13 cards. 41) A royal flush (5 highest cards of a single suit) in poker ) In poker, a full house (3 cards of one value, 2 of another value) ) In poker, four of a kind (4 cards of the same value) ) In bridge, 6 of one suit, 4 of another, and 3 of another

5 Solve the problem. 45) What is the probability that at least 2 of the 435 members of the House of Representatives have the same birthday? ) An elevator has 4 passengers and 8 floors. Find the probability that no 2 passengers get off on the same floor considering that it is equally likely that a person will get off at any floor ) 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 1 from town C ) A ring contains 8 keys: 1 red, 1 blue, and 6 gold. If the keys are arranged at random on the ring, find the probability that the red is next to the blue Find the requested probability. 49) A family has five children. The probability of having a girl is 1. What is the probability of having exactly 2 girls and 3 2 boys? ) A family has five children. The probability of having a girl is 1. What is the probability of having no girls? ) A family has five children. The probability of having a girl is 1. What is the probability of having no more than 3 boys? A die is rolled five times and the number of fours that come up is tallied. Find the probability of getting the given result. 52) Exactly zero fours ) Exactly two fours A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result. 54) More than one two At the University of Edmond (EU), 33% of the students were born outside of Oklahoma. Find the probability of the event from a random sample of 10 students from EU. 55) Exactly 2 were born outside of Oklahoma ) Exactly 4 were born in Oklahoma ) Seven or more were born outside of Oklahoma

6 Find the probability of the event. 58) A 10-question multiple choice test has 4 possible answers for each question. A student selects at least 6 correct answers by guessing all the answers ) The probability that a radish seed will germinate is.7. The gardener plants 20 seeds and she harvests 16 radishes ) A battery company has found that the defective rate of its batteries is.03. Each day, 22 batteries are randomly tested. On Tuesday, 1 is found to be defective

7 Answer Key Testname: MATH PRACTICE EXAM #2 1) C 2) A 3) C 4) C 5) A 6) C 7) D 8) A 9) B 10) B 11) A 12) D 13) D 14) D 15) C 16) B 17) D 18) A 19) D 20) C 21) B 22) A 23) B 24) D 25) D 26) C 27) B 28) A 29) A 30) A 31) D 32) A 33) D 34) B 35) B 36) B 37) A 38) A 39) C 40) A 41) A 42) D 43) C 44) C 45) D 46) D 47) A 48) D 49) A 50) C 51) B 52) B 53) A 54) C 55) B 56) D 57) A 58) C 59) C 60) C