STATISTICS MATHEMATICS (Statistics) 6. Problem 8. Problem Sixty people were contacted and responded to There are 20 seniors serving the student a movie survey. The following information was council of CTU-MC this year. Of these, 3 have 1. Problem 3. Problem obtained: not served before, 10 served on the council in From the following data: a. 6 people liked comedies, dramas and their junior years, 9 in their sophomore years, On the first six tests in her Mathematics 21, 13, 28, 50, 68, 56, 21, 32, 45, 43, 15 science fiction and 11 in their freshman years. There are 5 subject, her scores were 92, 78, 86, 92, 95, b. 13 people liked comedies and dramas. who served during both their sophomore and and 91. C. T Find the mean value. 10 people liked comedies and science junior year, 6 during both their freshman and a) 42.03 c) 32.52 @ Determine the median of her scores. fiction. junior years, and 4 during both their freshman 35.64 d) 46.11 a) 91.50 c) 92 d. 11 people liked dramas and science and sophomore years. How many seniors b) 88.5 d) 93.5 fiction. served on the student council during each of Find the median. e. 26 people liked comedies. the four years in high school? 32 0 45 f. 21 people liked dramas a) 2 c) b) 28 di 43 2 Determine the mode of her scores. b) 3 26 (e C) 91 g. 25 people liked science fiction. di Find the mode. 0) 95 1) 86 1) How many of these surveyed liked none of 43 C) 13 50 di 21 If she took a seventh test and raised the these categories PERMUTATION mean of her scores exactly one point, a) 11 Find the range. b) 20 di 16 what was her score on the 7th test? a) 43 2 41 9. Problem C) 99 55 di 53 a) 96 2 How many liked only comedies? b) 100 d) 97 a) 5 C) 9 You know that the extension of a private (5) Find the variance. b) 18 di 15 telephone number is 272 but you have a) 406.068 295.322 4. CE Board May 2013 orgotten the last 4 digits. You can only recall 360.950 324.855 How many liked only dramas? that the last 4 digits are 3, 6, 8, and 9 but you A set has 5 items and it has a range of 7. The a) 3 c) 4 Find the standard deviation set is composed of the following: d) 7 do not know the order. What is the maximum 17.18 c) 18.02 number of telephone calls you will need to (1, 2, M, 5, M2} with M > 0 0) 18.99 d) 20.15 make in order to dial the correct number? Find the average of the number set. a) 4.42 7. Problem 1) 24 C) 6 0) 5.31 2. b) 30 18 Problem bj 3.76 d) 2.55 In a high school graduating class of 100 From the given data shown: students, 54 studied mathematics, 69 studied VENN DIAGRAM 10. Problem history, and 35 studied both mathematics and Score 100 200 300 400 500 history. If one of these students is selected at How many 5-letter ordered codes can be Frequency 15 21 19 24 17 5. Problem random, find the probability that: ormed with letters A, B, C, and D if we allow @ the student took mathematics or history epeated use of the letter? 1 Find the mean value of the distribution. a) 1260 C) 985 3) 310.52 C) 324.17 In a group of 60 Civil Engineering students, 45 a) 0.62 c) 0.51 b) 1143 d) 1024 b) 313.82 1) 307 29 are taking Surveying, 30 are taking b) 0.88 d) 0.75 Mathematics, and 20 are taking both subjects. 2) Find the population variance of the A student is chosen at random, what is the the students did not take either of these distribution. probability that the student chosen is taking subjects 11. CE Board May 2014 a) 20292.92 18156.82 neither Surveying nor Mathematics? a) 0.03 C) 0.22 If you are given the word PARALLEL, compute 19165.55 d) 17967.66 b) 0.12 d) 0.36 the number of different 8-letter arrangements @ Find the standard deviation of the K - @ the student took history but not can be formed. distribution. mathematics a) 3000 C) 3150 134.04 138.43 a) 0.80 c) 0.34 ) 3360 d) 3240 b) 142.45 d) 126.64 b) 0.12 d) 0.58MATHEMATICS (Statistics) 2 12. CE Board Nov. 2012 COMBINATION @ Find the number of ways the class can @ one is brass and one is steel elect a president, a vice-president, a) 0.5623 C) 0.9736 In a certain city in the Philippines, all seven treasurer, and secretary. d) 0.0452 digit telephone numbers begin with 350. How 17. Problem b) 0.1939 a) 573 ways c) 555 ways many telephone numbers maybe assigned to b) 536 ways di 540 ways 24. A committee of 5 members is to be randomly CE Board May 2014 that city if the last four digits should not begin CE Board May 2015 or end in zero? selected from a group of 9 engineers and 20 a) 8285 ") 8560 lawyers. Determine how many different 21. CE Board May 2015 A classroom contains 71 students. 10 of them b) 8400 d) 8100 committees can be formed if 2 members must be an engineer and 3 members must be Ayala Corporation advertised to hire financial are Chinese, 24 are Japanese and 37 are lawyers. analyst. The company received applications Filipinos. If three students are randomly asked a) 42880 from 10 candidates who seem to be equally to get out of the room, one after the other, 13. Problem C) 43600 b) 40530 41040 qualified. The company manager has decided what are the probabilities that A particular classroom in CIT-U has 24 seats to call only 3 candidates for an interview. If @ All 3 students are Chinese? and 24 students. Assuming the seats are not 18. CE Board Nov. 2009 she randomly selects 3 candidates from the a) 0.0045 C) 0.0013 moved, how many different seating 10, how many total selections are possible? bj 0.0021 d) 0.0039 arrangements are possible? In a lotto, there are 30 pingpong balls, how a) 14 c) 110 a) 7.50 x 1023 ) 4.10 x 1023 many possible combinations if 5 balls are b) 130 d) 120 2 All 3 students are Japanese? drawn out at a time? ) 5.30 x 1023 d) 6.20 x 1023 a) 0.0253 C) 0.0185 a) 142,506 C) 143,679 b) 0.0592 d) 0.0354 b) 145,193 d) 141,082 22. Problem 14. Problem @ All 3 students are Filipinos? 19. Problem There are 13 teams in a tournament. Each eam is to play with each other only once. a) 0.1359 :) 0.3592 How many permutations are there if the letters b) 0.2433 d) 0.4408 In a pre-board examination a reviewee may What is the minimum number of days can they PNRCSE are taken six at a time? choose to solve 8 out of 12 problems in order all play without an team playing more than one a) 710 c) 730 25. game in any day? CE Board Nov. 2013 to pass the exams. In how many ways can the b) 720 d) 760 a) 10 CE Board May 2015 reviewee choose them? c) 12 1) 502 C) 481 bj 11 The probability that a construction generator 15. Problem b) 511 1) 495 will operate satisfactorily for 5 yrs is 0.80 and 20. CE Board Dec. 2014 PROBABILITY OF DEPENDENT that a welding machine will operate Four different colored flags can be hung in a satisfactorily over the same period of time is row to make a coded signal. How many & INDEPENDENT EVENTS A concrete design class contains 10 students 0.75. Find the probabilities that in a 5 year signals can be made if a signal consists of the period. with 6 men and 4 women. They decided to display of one or more flags? organize for the coming intramurals by 23. CE Board May 2014 1 Both generator and welding machine a) 65 C) 66 b) 64 di 62 creating committees to take care of the A box contains washer, 24 of which are brass, operate satisfactorily. preparations. 36 copper, the remainder are steel. One a) 0.35 c) 0.51 b) 0.60 d) 0.48 @ Find the number of ways a 4-member washer is taken at random, retained and a 16. Problem committee can be formed. second washer similarly drawn. Determine the Only the Four couples are to eat at a round table with a) 245 c) 231 probability that generator operate satisfactorily 0) 210 1 183 the men and women alternating, If the hostess both washers are steel a) 0.5 C) 0.8 reserves a place for herself, in how many a) 0.2691 c) 0.0368 b) 0.2 di 0.6 2 Find the number of ways a 4-member b) 0.3115 ways can she assign seats to the others? d) 0.1576 committee can be formed with 2 men and a) 120 160 3 Only the welding machine will operate b) 100 d) 144 2 women @ first is brass and the second is copper. satisfactorily. a) 90 C) 66 a) 0.0873 c) 0.1092 a) 0.27 C) 0.34 b) 75 d) 80 b) 0.0349 d) 0.0568 b) 0.20 d) 0.15MATHEMATICS (Statistics) 3 26. CE Board May 2014 CONDITIONAL PROBABILITY 1 A red marble 4) Vibration and high resistance 3 nsists of three concentric C) a) 50000 100000 circles with different radii 1, 3 and 5 units. If a Problem dart thrower always hits the area of a 5-unit 3 radius but hit the area randomly, what is the The probability that a randomly selected bl 50000 50000 probability that a dart hits the area of between student from a college is a senior is 0.20, and the 1 unit radius circle and the 3 unit radius the joint probability that a student is a civil circle? engineering student and a senior is 0.03. Find @ A blue or green marble the conditional probability that a student 33. Problem 11 C) selected at random is a civil engineering 3- WIN student and hershe is a senior. Seventy two percent of a town's voters favor a) 0.33 C) 0.24 the recycling issue, 12% opposes it and 16% b) 0.15 d) 0.47 are neutral, What is the probability that a randomly selected voter from this town will 29. Problem @ A red or blue marble either favor recycling or be neutral? a) 0.66 0) 0.59 27. CE Board Dec. 2014 The probability that an adult has a lung cancer b) 0.75 d) 0.86 is 0.02. The probability that an adult is a O- WIN A box contains 15 billiard balls, which are smoker and has a lung cancer is 0.009. Find numbered 1 to 15. A ball is drawn at random the conditional probability that a randomly 34. CE Board Nov. 2011 and the number is written down. Determine selected adult is a smoker given that this the following probabilities The probability of event x happening is 3/5. person has lung cancer. 32. Problem C) 0.66 The probability of another event y happening That the number is less than 5 a) 0.45 b) 0.58 d) 0.32 When testing 1000 soldered joints, 4 failed IS 2/3 during a vibration test and 5 failed due to high (@ Find the probability that both events x and E C) 15 30. Problem resistance. Determine the probability of a joint y will happen. failing due to: D Find P(A) if P(A or B) = 0.308, C) P(A) = 0.076 if A and B are mutually @ Vibration alt uil- exclusive events. 2) That the number is even and less than 5 a) 0.186 C) 0.458 C) 1 bi 6) 0.232 1 0.395 250 250 a 3 3 Find the conditional probability that B will bl 2 Find the probability that only x will happen. 250 200 occur given A has occurred if P(A) = 0.80, al - P(A and B) = 0.20 High resistance onIN wl- a) 0.25 c) 0.32 @ That the number is even or less than 5 b) 0.66 1) 0.41 200 200 E PROBABILITY OF MUTUALLY 7 1 di Find the probability that either event x and EXCLUSIVE EVENTS 200 200 event y will happen. bl 31. Problem @) Vibration or high resistance 3 a A jar contains 2 red marbles, 3 blue marbles, 1000 1000 and 1 green marbles. Find the probability of 9 randomly drawing the given type of marble. bi 100 1000