Which Venn diagram below best represents the relationship between the sets A, B, and C?

Transcription

1 Review material for mth 245 midterm chap A,,,, B,,,,, C,, Which Venn diagram below best represents the relationship between the sets A, B, and C? a. b. B B A C A C c. d. B B A C A C e. None of the above

2 2. A certain number of students were asked if they owned a computer and/or a car. Of the students asked, 85 of them had a computer, 118 of them had a car, 62 of them had both, and 15 had neither. How many students were asked? a. 156 b. 218 c. 141 d. 203 e. Cannot be determined from the given information 3. Five friends decided to drive together to a temporary employment agency. After taking their assessment tests they discovered that three of them all qualified for a list of 10 distinct job openings and the other two friends both qualified for a list of 6 distinct job openings. None of the jobs on the list of 10 are the same as those on the list of 6 and all the jobs are different. How many different ways can the 5 friends be assigned to temporary jobs (assuming everyone gets one job)? a. P(16,5) = 524,160 b. P(10,3) + P(6,2) = 750 c. C(16,5) = 4,368 d. P(10,3)P(6,2) = 21,600 e. None of the above. 4. The five friends drive to the employment agency as they did in problem 8. However, this time suppose after their assessment tests they are told that they all qualify to work night shift at the food cannery. The problem is there are only 4 of these jobs available. How many different ways can the 5 friends be assigned to the 4 jobs (assuming no one gets more than one job and one person gets no job)? a. C(5,4) = 5 b. P(5, 4) = 120 c. C(5,1) = 5 d. (5)(4)(3)(2) = 120 e. None of the above.

3 5. A box contains 8 red balls and 10 yellow balls. How many different ways can two balls be randomly selected with the two balls being the same color? a. C(8,2)C(10,2) b. C(18,2) c. C(18,1) + C(17,1) d. C(8,2) + C(10,2) e. None of the above 6. How many different numbers can be formed by rearranging the digits of 858,585,555? a. 362,880 b. 504 c. 20,160 d. 36 e A phone number (without the area code) consists of 7 digits from 0 through 9 and digits may be repeated. If all the phone numbers in Brownsville, Oregon have the first three digits 466, how many different phone numbers are possible? a. 10,000,000 b. 10,000 c. 4,782,969 d. 6,561 e. 5,040

4 8. For certain sets A and B, n A B 53 n B 35 n A B 8. Find n(a). a. 26 b. 18 c. 46 d. 27 e. None of the above 9. Marla s mom will let her select a puppy, a kitten, or a hamster. If there are 15 puppies, 12 kittens, and 9 hamsters in the pet store in how many different ways can Marla select one pet to take home? a. 1,620 b. 36 c. 27 d. 45 e. 180

5 10. If the Universal set U={a, b, c, d, e, f, g, h}, set A={b, d, e, f} and set B={a, b, e, g,}, then the set a){c, h} ( A B)' =? b){a, b, d, e, f, g, h} c){a, c, d, f, g, h} d){a, d, f, g} e){b, c, e, h} cars were parked in the lot at 11:48 pm on Saturday night. 553 of them were green. 357 of the cars had nice wheels. 213 of them were green and had nice wheels. How many cars in the lot were green and did not have nice wheels? a) 553 b) 340 c) 213 d) 157 e) There are 35 people on a baseball team. In how many ways can the positions of pitcher, catcher, center fielder and shortstop be assigned? a) 31, 465 b) 52, 360 c) 755,160 d) 1,256,640 e) 38,955,840

6 13. In the expansion of a) 70 b) 495 c) 1680 d) 11,880 e) There is no term with 12 ( a b), what is the coefficient of the a 8 b 4 in it in the expansion a 8 b 4 term? 14. A coin is tossed 10 times. How many sequences of 7 heads and 3 tails are possible? a) 120 b) 210 c) 720 d) 604,800 e) 39,916, In the Venn diagram to the right, the numbers refer to the number of elements. n A C '? U 5 A a) 10 b) 44 c) d) 52 e) 26 B C

7 16) A club consists of 12 democrats and 17 republicans. A committee is formed with 4 democrats and 4 republicans, how many different committees could be formed? a) 495 b) 2,380 c) 1,178,100 d) 4,292,145 e) 173,059,286,400 17) A box has 9 apples and 6 oranges in it. In how many ways can you choose 10 pieces of fruit of which at least 7 are apples? a) 34,836,480 b) 32,659,200 c) 861 d) 855 e) ) For the sample space {A, B, C, D} we are told P(A) = 0.25, P(B) = 0.30, P(C) = Find P(D). a b c. 0 d e. 0.05

8 19) A box contains 12 red balls and some black balls. One ball is randomly selected and the probability it is red is 3/11. What is the total number of balls in the box (red and black)? a. 44 b. 32 c. 12 d. 11 e. None of the above 20) How many different five-letter words can be formed from the letters in the set {B, C, H, O, Z, L, Y}if no repeated letters are allowed? a. 21 b. 16,807 c d e ) How many different ways can a company select a group of 3 receptionists from an applicant pool of 17 receptionists? a. 680 b c d. 6 e. None of the above

9 22) A company stores its product in two warehouses, A and B. It has been observed that a worker sent to get an item from a warehouse will go to warehouse A 60% of the time and to warehouse B 40% of the time. Suppose we know that 5% of the items in warehouse A are defective and 8% of the items in warehouse B are defective. If a worker is sent to get an item and the item turns out to be defective, find the probability they got the item from warehouse A. Round your answer to three decimal places. a b c d e ) Given two events E and F such that P E 0.6, P F 0.5, P E F find E F P. a. 1.1 b c d e. None of the above

10 24) With a certain scratch-off lottery ticket a player can either win $100 or win nothing. The probability that a person wins $100 on a single ticket is If Andy buys 10 tickets, what is the probability of winning $100 each on 2 of the 10 tickets? Round your final answer to 5 decimal places. a b c d e. None of the above 25) Suppose A and B are nonempty sets from the same universe U and A B. True or False? B A a. True b. False c. Not enough information is given 26) Twenty balls are numbered 1 through 20 and placed in a box. A ball is randomly selected and placed back into the box. Then a second ball is randomly selected. What is the probability that the first ball s number is evenly divisible by 4 and the second ball s number is odd? a. 0.5 b c d e

11 n B C 27) Given the universe U with sets A, B, and C as shown below, find. U 400 A B C a. 429 b. 4 c. 404 d. 431 e. 400

12 28) One morning 40 employees were in the company cafeteria. 20 used cream in their coffee, 25 used sugar, and 15 used both. Determine whether or not the events used cream and used sugar are independent. a. Yes, they are independent b. No, they are dependent c. Cannot determine from the given information 29) For two events E and F, P E 0. 42, P F 0. 81, and E F Find F E. P Round your answer to three decimal places. P. a b c d e. None of the above 30) Urn A contains 4 white balls and 6 black balls. Urn B contains 3 white balls and 5 black balls. A ball is drawn from urn A and then transferred to urn B. After that a ball is drawn from urn B. What is the probability the transferred ball was black given that the second ball drawn was white? (Round your answer to the nearest hundredth.) a) 0.53 b) 0.57 c) 0.47 d) 0.38 e) none of the above

13 Survey results: use for questions Do not drink coffee Prefer reg. coffee Prefer decaf. Total Female Male total A student is chosen at random from the group surveyed, find the probability that the student: 31) does not drink coffee a. 41/497 b. 260/497 c. 145/497 d. 46/260 e. 46/115 32) is male a. 41/497 b. 260/497 c. 145/497 d. 46/260 e. 46/115 33) is a female who prefers regular coffee a. 41/497 b. 260/497 c. 145/497 d. 46/260 e. 46/115

14 34) prefers decaf, given that the student was chosen from the male students a. 41/497 b. 260/497 c. 145/497 d. 46/260 e. 46/115 35) is male, given that the student prefers decaf. a. 41/497 b. 260/497 c. 145/497 d. 46/260 e. 46/115 36) is female given that the student prefers regular or does not drink coffee a. 41/497 b. 168/382 c. 145/497 d. 46/382 e. 46/115

15 37) If the Universal set U={a, b, c, d, e, f, g, h}, set A={b, d, e, f} and set B={a, b, e, g,}, then the set ( A' B) =? a){c, h} b){a, b, d, e, f, g, h} c){a, c, d, f, g, h} d){a, g} e){b, c, e, h} 38) A box contains 15 parts of which 4 are defective. 2 parts are chosen at random from the box. What is the probability that both are defective? a) b) c) d) e) A medical research team selects 5 patients at random from a group of 15 patients for special treatment. In how many different ways can the patients be selected? a.3,003 b. 3,628,800 c. 36,036 d. 120 e. none of the above

16 40. One student representative is chosen from each of 4 clubs. In how many different ways can the 4 students be selected, given the following number of members in each club? Rodeo has 40, Kite has 27, Frisbee has 85, and Canoeing has 34. a. 14,665,800 b. 78,560 c. 3,121,200 d. 186 e. none of the above 41. A program consists of 4 musical numbers and 3 speeches. In how many ways can the program be arranged so that it begins and ends with a musical number? a. 144 b. 5,040 c. 784 d. 1,440 e. none of the above

17 42. A poll was conducted to see how many teens have TVs, radios and computers. The results were: Item number TV 39 R 73 C 10 TV and R 22 C and R 3 TV and C 4 TV and R and C 2 How many had exactly 2 of the 3 items? a. 23 b. 25 c. 3 d. 15 e. none of the above 43. A survey of working couples in a county revealed that the probability the husband is happy with his job is 0.72, the probability the wife is happy with her job is 0.55, and the probability both are happy with their jobs is A working couple is selected at random. Find the probability that neither one is happy with his/her job. a) 0.92 b) 0.08 c) 0.37 d) 0.20 e) none of the above