Study Guide for Test III (MATH 1630) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the number of subsets of the set. 1) {x x is an even number between 19 and 39} A) 1024 B) 128 C)7 D) 38 1) Insert " " or " " in the blank to make the statement true. 2) {5, 7, 9} {x x is an odd counting number} A) B) 2) 3) {e, d, j, h} {e, d, j, h, m} A) B) 3) 4) Jose is applying to college. He receives information on 9 different colleges. He will apply to all of those he likes. He may like none of them, all of them, or any combination of them. How many possibilities are there for the set of colleges that he applies to? A) 9 B) 508 C)16 D) 512 4) Shade the Venn diagram to represent the set. 5) A' B' 5) A) B) C) D) 1
6) (A B C')' 6) A) B) C) D) Use the union rule to answer the question. 7) If n(a) = 10, n(a B) = 28, and n(a B) = 6; what is n(b)? A) 23 B) 18 C)25 D) 24 7) 8) If n(a) = 6, n(b) = 13, and n(a B) = 4; what is n(a B)? A) 14 B) 15 C)19 D) 16 8) Use a Venn Diagram and the given information to determine the number of elements in the indicated region. 9) n(u) = 114, n(a)= 36, n(b) = 56, n(a B) = 13, n(a C) = 16, n(a B C) = 7, n(a' B C') = 36, and 9) n(a' B' C') = 27. Find n(c). A) 8 B) 17 C)24 D) 31 Use a Venn diagram to answer the question. 10) At East Zone University (EZU) there are 627 students taking College Algebra or Calculus. 417 are taking College Algebra, 261 are taking Calculus, and 51 are taking both College Algebra and Calculus. How many are taking Algebra but not Calculus? A) 576 B) 366 C)315 D) 210 10) 2
11) A survey of 128 college students was done to find out what elective courses they were taking. Let A = the set of those taking art; B = the set of those taking basket weaving; and C = the set of those taking canoeing. The study revealed the following information: n(a) = 45; n(b) = 55; n(c) = 40; n(a B) = 12; n(a C) = 15; n(b C) = 23; n(a B C) = 2. How many students were not taking any of these electives? A) 10 B) 38 C)46 D) 36 11) Write the sample space for the given experiment. 12) A card is selected at random from a deck and its suit is recorded. Then a coin is tossed. A) {(4, 2)} B) {(club, diamond, heart, spade, head, tail)} C){(head, spade), (head, club), (head, heart), (head, diamond), (tail, spade), (tail, club), (tail, heart), (tail, diamond)} D) {(spade, head), (club, head), (heart, head), (diamond, head), (spade, tail), (club, tail), (heart, tail), (diamond, tail)} 12) A die is rolled twice. Write the indicated event in set notation. 13) The first roll is a 4. A) {(4, 3)} B) {(4, 1), (4, 2), (4, 4), (4, 5), (4, 6)} C){(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)} D) {(4, 1), (4, 3), (4, 5)} 13) 14) The sum of the rolls is 8. A) {(2, 6), (3, 5), (5, 3), (6, 2)} B) {(4, 4)} C){(2, 6), (3, 5), (4, 4)} D) {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)} 14) Find the probability of the given event. 15) A single fair die is rolled. The number on the die is greater than 2. 15) A) 1 6 B) 2 3 C) 1 3 D) 5 6 Find the probability. 16) When a single card is drawn from a well-shuffled 52-card deck, find the probability of getting a red card. 1 A) 2 B) C) 1 D) 1 52 2 4 16) Find the probability of the given event. 17) A single fair die is rolled. The number on the die is a multiple of 3. 17) A) 1 6 B) 1 3 C) 1 36 D) 1 2 Find the probability. 18) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a heart, club, or diamond? A) 3 4 B) 12 13 C)3 D) 48 52 18) 3
19) A bag contains 6 red marbles, 9 blue marbles, and 4 green marbles. What is the probability that a randomly selected marble is blue? A) 9 4 B) C) 3 6 D) 19 19 5 19 19) 20) A lottery game has balls numbered 1 through 19. What is the probability that a randomly selected ball is an even numbered ball or a 4? A) 9 B) 19 C) 4 D) 9 19 4 19 20) Find the indicated probability. 21) The age distribution of students at a community college is given below. 21) Age (years) Number of students (f) Under 21 414 21-25 412 26-30 216 31-35 52 Over 35 22 1116 A student from the community college is selected at random. Find the probability that the student is at least 31. Round your answer to three decimal places. A) 74 B) 0.066 C) 0.934 D) 0.047 22) The distribution of B.A. degrees conferred by a local college is listed below, by major. 22) Major Frequency English 2073 Mathematics 2164 Chemistry 318 Physics 856 Liberal Arts 1358 Business 1676 Engineering 868 9313 What is the probability that a randomly selected degree is in Engineering? A) 0.1028 B) 0.0012 C) 0.0932 D) 868 Determine whether the given events are mutually exclusive. 23) Going to the beach and staying home at 2 pm on your birthday A) Yes B) No 23) 24) Being a teenager and being a United States Senator A) Yes B) No 24) 4
Find the indicated probability. 25) Find the probability that either a 6 or a 3 is obtained when a fair die is rolled. A) 2 B) 1 2 C) 1 3 D) 1 25) 26) Find the probability that the sum is no more than 6 when two fair dice are rolled. A) 17 5 B) C) 7 36 12 18 D) 7 36 26) 27) When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that either doubles are rolled or the sum of the dice is 4. A) 1 7 B) C) 2 1 D) 4 36 9 36 27) 28) When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that the first die is 3 or that doubles are rolled. A) 5 B) 11 C) 1 D) 1 18 36 36 3 28) Use a Venn diagram to find the indicated probability. 29) If P(A B) = 0.63, P(A) = 0.32, and P(B) = 0.46, find P(A B). A) 0.27 B) 0.56 C) 0.15 D) 0.11 29) 30) Suppose P(B) = 0.72, P(C) = 0.47, and P(B C) = 0.32. Find P(B' C'). A) 0.58 B) 0.68 C) 0.26 D) 0.55 30) Find the odds. 31) Find the odds in favor of drawing a 1 when a card is drawn at random from the cards pictured below. 31) A) 1 to 4 B) 4 to 1 C)1 to 5 D) 5 to 1 32) Find the odds in favor of drawing an even number when a card is drawn at random from the cards shown below. 32) A) 5 to 2 B) 2 to 3 C)3 to 2 D) 2 to 5 33) A survey revealed that 38% of people are entertained by reading books, 27% are entertained by watching TV, and 35% 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. A) 35% B) 100% C) 30% D) 65% 33) 5
34) A poll is conducted in a U.S. city to determine voting preferences prior to a presidential election. The following probabilities were obtained from the relative frequencies: P(D) = 0.51, P(M D) = 0.22, P(M D) = 0.77 where M represents male and D represents a person who plans to vote Democrat. Find P(M' D). A) 0.74 B) 0.52 C) 0.29 D) 0.49 34) 35) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd. 35) A) 1 2 B) 1 C)0 D) 1 6 36) 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. A) 26 51 B) 22 23 C) 4 17 D) 25 51 36) Find the indicated probability. 37) Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that both marbles are red. A) 1 4 B) 3 56 C) 1 28 D) 1 16 37) 38) Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that both marbles are white. A) 3 B) 3 C) 9 3 D) 28 8 56 32 38) 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? A) 0.01 B) 0.64 C) 0.51 D) 0.80 39) 40) A calculator requires a keystroke assembly and a logic circuit. Assume that 96% of the keystroke assemblies and 88% of the logic circuits are satisfactory. Find the probability that a finished calculator will be satisfactory. Assume that defects in keystroke assemblies are independent of defects in logic circuits. A) 0.7744 B) 0.9200 C) 0.9216 D) 0.8448 40) 41) 38% of a store's computers come from factory A and the remainder come from factory B. 1% 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) 0.04 B) 0.66 C) 0.015 D) 0.025 41) 6
42) 56% 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 1% 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) 0.011 B) 0.984 C) 0.98 D) 0.549 42) Find the probability. 43) 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. 43) A) 1 B) 1 2 C) 1 8 D) 1 4 44) Assuming that boy and girl babies are equally likely, find the probability that a family with four children has all boys given that the first is a boy. 44) A) 1 16 B) 0 C) 1 8 D) 1 4 Solve the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary. 45) For two events M and N, P(M) = 0.5, P(N M) = 0.6, and P(N M') = 0.5. Find P(M N). A) 0 B) 1.0 C)0.55 D) 0.45 45) 46) For mutually exclusive events X1, X2, and X3, let P(X1) = 0.26, P(X2) = 0.25, and P(X3) = 0.49. Also, P(Y X1) = 0.40, P(Y X2) = 0.30 and P(Y X3) = 0.60. Find P(X3 Y). A) 0.16 B) 0.62 C) 0.41 D) 0.22 46) Use Bayes' rule to find the indicated probability. 47) 53% of the workers at Motor Works are female, while 31% of the workers at City Bank are female. If one of these companies is selected at random (assume a 50-50 chance for each), and then a worker is selected at random, what is the probability that the worker is female, given that the worker comes from City Bank? A) 26.5% B) 15.5% C) 53% D) 16.4% 47) 48) Two stores sell a certain product. Store A has 44% of the sales, 5% of which are of defective items, and store B has 56% of the sales, 3% of which are of defective items. The difference in defective rates is due to different levels of pre-sale checking of the product. A person receives a defective item of this product as a gift. What is the probability it came from store B? A) 0.5641 B) 0.4308 C) 0.42 D) 0.55 48) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 49) To find P(A B) using Bayes' theorem, what conditional probability occurs in the numerator? 49) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 50) Suppose there are 5 roads connecting town A to town B and 8 roads connecting town B to town C. In how many ways can a person travel from A to C via B? A) 64 ways B) 40 ways C)13 ways D) 25 ways 50) 7
Write the sample space for the given experiment. 51) A box contains 2 blue cards numbered 1 through 2, and 3 green cards numbered 1 through 3. A blue card is picked, followed by a green card. A) {7} B) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2)} C){(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3)} D) {12} 51) 52) How many 6-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions of digits are allowed? A) 899,999 six-digit numbers B) 900,000 six-digit numbers C) 46,656 six-digit numbers D) 1,000,000 six-digit numbers 52) How many distinguishable permutations of letters are possible in the word? 53) BASEBALL A) 20,160 B) 5040 C) 10,080 D) 40,320 53) 54) GIGGLE A) 720 B) 4320 C)120 D) 36 54) 55) How many ways can a committee of 2 be selected from a club with 12 members? A) 2 ways B) 66 ways C)132 ways D) 33 ways 55) 56) A group of five entertainers will be selected from a group of twenty entertainers that includes Small and Trout. In how many ways could the group of five include at least one of the entertainers Small and Trout? A) 6936 ways B) 15,504 ways C) 11,628 ways D) 8568 ways 56) Decide whether the situation involves permutations or combinations. 57) A batting order for 9 players for a baseball game. A) Permutation B) Combination 57) 58) A blend of 2 spices taken from 8 spices on a spice rack. A) Permutation B) Combination 58) 59) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how many ways can you get 4 apples? A) 10 ways B) 8 ways C)15 ways D) 5 ways 59) Find the requested probability. 60) A family has five children. The probability of having a girl is 1/2. What is the probability of having exactly 2 girls and 3 boys? A) 0.0312 B) 0.6252 C) 0.3125 D) 0.0625 60) 61) A family has five children. The probability of having a girl is 1/2. What is the probability of having at least 4 girls? A) 0.1563 B) 0.1875 C) 0.3125 D) 0.0313 61) 8
62) A coin is biased to show 39% heads and 61% tails. The coin is tossed twice. What is the probability that the coin turns up tails on both tosses? A) 37.21% B) 22% C) 39% D) 61% 62) Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the probability. 63) Three coins are tossed, and the number of tails is noted. 63) A) B) C) D) x P(x) 0 3/16 1 5/16 2 5/16 3 3/16 x P(x) 0 1/8 1 3/8 2 3/8 3 1/8 x P(x) 0 1/3 1 1/6 2 1/6 3 1/3 x P(x) 0 1/6 1 1/3 2 1/3 3 1/6 Find the requested probability. 64) A coin is biased to show 41% heads and 59% tails. The coin is tossed twice. What is the probability that the coin turns up heads on the second toss? A) 41% B) 24.19% C) 59% D) 16.81% 64) 9
Answer Key Testname: UNTITLED1 1) A 2) B 3) A 4) D 5) B 6) C 7) D 8) B 9) D 10) B 11) D 12) D 13) C 14) D 15) B 16) C 17) B 18) A 19) A 20) A 21) B 22) C 23) A 24) A 25) C 26) B 27) C 28) B 29) C 30) B 31) A 32) B 33) C 34) A 35) C 36) D 37) C 38) A 39) C 40) D 41) D 42) D 43) B 44) C 45) C 46) B 47) B 48) B 49) P(B A) 50) B 10
Answer Key Testname: UNTITLED1 51) C 52) D 53) B 54) C 55) B 56) A 57) A 58) B 59) D 60) C 61) B 62) A 63) B 64) A 11