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Directions: Identify what is being asked in each question. Write your answer in your paper. 1. How many ways can three boys and three girls be arranged in a circle if the girls must remain next to each other? A. 6 B. 24 C. 36 D. 72 2. How many different arrangements can be formed from the letters of the word, EQUATION if Each arrangement begins and ends with a consonant? A. 720 B. 2,040 C. 3,100 D. 4,320 3. A Math teacher has 3 Algebra books, 5 Geometry books, 4 Trigonometry books, and 3 Statistics books. If Statistics, Trigonometry, Algebra, then Geometry books are arranged in that order, in how many ways can this be done? A. 54,305 B. 88,000 C. 103,680 D. 2,438,320 4. A bucket contains 14 marbles in which 4 are red, 3 are blue, 4 are green, and 3 are yellow. How many sets of 4 marbles are there in which none are red, but at least 2 are green? A. 115 B. 303 C. 654 D. 315 5. Out of 5 mathematicians and 7 engineers, a committee consisting of 2 mathematicians and 3 engineers is to be formed. In how many ways can this be done if two particular mathematicians cannot be in the committee? A. 70 B. 105 C. 450 D. 915 6. Three coins are tossed. Find the probability of getting at least 1 tail. A.78 3.67 C56 0.45 7. A box contains 7 blue marbles, 6 red marbles, and 4 white marbles. If a marble is picked at random, what is the probability that it is blue marbles? A.417 3.617 0.717 D.413 8. A committee of three is to be chosen at random from a group of 5 students consisting of 3 boys and 2 girls. What is the probability that a committee consisting of 2 boys and 1 girl will be chosen? A.110 3.15 0.310 D.35 9. There are x + 5 red balls, x blue balls, and x + 10 white balls in a box. One ball is selected at random from the box. If the probability that the selected ball is blue is equal to 1 8 , what is the value of x? A. 2 B. 3 C. 4 D. 5 10. In number 4, there are x + 5 red balls, x blue balls, and x -I- 10 white balls in a box. One ball is selected at random from the box. If the value of x is 12, what is the probability that the selected ball is white? A. 1251 B. 1751 C. 2251 D. 29 51 11. A card is drawn at random from a standard pack 0152 playing cards. Find the probability that the card is a diamond or a queen. A. 1352 B. 12 C. 313 D.413 12. The probabilities of three teams. SLHS, MHS, and EHS winning a basketball competition are 1 4 , 1 7' , and 1 8 respectively. Assuming only one team can win, calculate the probability that neither SLHS or EHS wins. A.58 B.49 C310 D.211 13. A die is rolled. What is the probability of getting a prime number or a factor of 6? 14. Twenty balls in a jar are numbered from 1 to 20. A ball is drawn at random. Find the probability that the number on the ball is less than 11 or greater than 15. A.23 B.34 6.45 D.56 15. The LSI or Locally Stranded Individual has a 95% chance that can avail \"Balik Probinsya Program" if assisted by their LGU, 50% chance if they rely on DSWD, and an 80% chance on both. What is the probability that they will reach their province by relying on LGU or DSWD? A. 95% B. 85% C. 75% D. 65% GWEN: Ameiia has a deck of 52 cards. She randomly seiects one card and considers the ioiiowing events: Event A: picking a card that is a heart; Event 3: picking a card that is biack Event c: picking a card that is not a spade 16. Are events A and B mutually exclusive? A. Yes B. No C. Maybe D. No answer 17. Are events A and C mutually exclusive? A. Yes B. No C. Maybe D. No answer 18. I roll a regular six-sided die. What is the probability that the score is an odd or prime number? A.13 B.12 C.23 D34 19. Suppose A, B, and C are three mutually exclusive events in a sample space 3. Given that S=AUBUC, (A)=1 5 P(B), and P(C)=4P(A), find P(AUC). A.23 B12 C13 D15 20. Let A and B be two mutually exclusive events. Given that (A)=0.25 and P(AUB) =0.?7, determine P(B). A. 1.02 B. .92 C. .62 D. .52 21. What is the probability of getting exactly 3 heads in 8 ips of a fair coin. A. 1256 B. 3256 C. 13 D. 732 22. There are 7 students in a class: 2 boys and 5 girls. If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a girl? A.1504 B184 C.17 DZ? 23. Jason, Hans, and Jose and 4 other students are left in drawing for 3 DVD's. What is the probability that Jason, Hans, and Jose will each win a DVD? A. 135 B. 1120 C. 1210 D.1?20 24. A 4-digit PIN is selected. What is the probability that there are no repeated digits? A.1 1000 B. 21 1000 C. 63125 D. 1 4 25. Compute the probability of randomly drawing five cards from a deck and getting exactly one Ace. A. 3243 10829 B. 3243 21658 C. 3243 54145 D. 3243 108290 26. You roll a fair six-sided die twice. The first roll shows a five and the second roll shows a six. A.136 B.130 C16 D12 27. There were 12 pink, 7 purple and 9 yellow owers in a vase. You randomly choose a flower from the vase to take home. Your friend randomly chooses another flower from the vase to take home. What is the probability that you choose a purple flower and your friend chooses a yellow flower? A.9112 B. 734 C. 27196 D. 17 28. In a certain company, the probability that an employee is married is 65%. The probability that an employee owns a car is 30%. What is the probability that the employee is married and owns a car? A. 19.5% B. 35% C. 46.15% D. 95% 29. A iar contains 3 red, 5 green, 2 blue and 6 yellow marbles. A marble is chosen at random from the jar. After replacing it, a second marble is chosen. What is the probability of choosing a green and then a yellow marble? A.1? B.215 C. 13 D. 15128 30. A card is drawn from a deck of cards. Then the card is replaced, the deck is reshuffled, and a second card is drawn. What is the probability of getting a 3 on the rst draw and a red card on the second draw? A.1169 B. 3104 C. 126 D. 16