1. A bag contains three green marbl marbles, and nwo orange marbles. Ifa marble is picked at random, what is the probability that an orange marble will NOT be picked? at . What is the probability that a number selected at random from the set of numbers above will be the average of the set? (A) 0 1 B) ® 1 Os ~ 3 (@) To 2 () 3 ur blue. PROBABILITY 3. If the probability that an event will coy, is © and x # 0, what is the probability that this event will NOT occur ? l-x (A) a 4-x 2 a @) © w4 : ®) Questions 4 and 5. A jar contains only red, blue, and green marbles. The probability of picking a red_ marble is 0.25, and the probability of picking a blue marble is 0.40. 4. What is the probability of picking a green marble? (A) 0.25 (B) 0.35 (©) 0.60 (D) 0.75 (E) 1.00 - What is the LEAST number of marbles that could be in the jar? (A) 4 (B) 5 (© 10 (D) 20 () Ik cannot be determined from the information given,‘A six-sided cube whose faces are " umbered from 1't0 6 is rolled twice. Which of the following statements must be true? |. There are 36 possible outcomes. Il. The probability that the two numbers rolled do nor match is. Il. The probability hat the sum of the two numbers rolled is 5 is 4 7 (A) Lonly (B) I only (© Iand I only (D) [and III only (E) Mand IIT only . If che leters L, O, G, I, and Care randomly arranged to form a five-letrer. “word,” what is the probability thar the “Fesule will be the word LOGIC? a) ia (B) x 1 Oz us 1 OF 1 (E) = ®> VAN The circle above is divided into eight sectors of equal area. What is the probability chat the spinner will land on an even-numbéted region in each of two consecutive spins? “) 3 @ 3 64 ©@3 8 ot 4 @ 2, 64 ). Three fair coins are tossed at the same time. What is the probability that all chree Coins will come up heads or all will come up tails? + 8 wi é ol m+ @310. The faces ofa red cube and a yellow cube are numbered from 1 to 6. Both cubes are rolled, What is the probability thac the top face of each cube will have the same number? 1 ws 1 (B) é Oz (D) = ere «@ + 2 . Ajar contains 54 marbles each of which is blue, green, or white. The probability of selecting a blue marble at random from the jar is 4, and the probability of selecting a green marble at random is ¢, How many white marbles does the jar contain? (A) 6 (B) 8 (9 (D) 12 (E) 18 A= {-2, -1,0,1,2} |. If x represents a number picked at random from set A above, what is the probability that x? < 2? 13. If x represents a number picked at random from the set {~3, ~2, ~1, 0, 1, 2}, what is the probability that x will satisfy the “inequality 4 — 3x < 6? 1 @ é 1 Bs 1 5 2 oO; 5 (E) é A= (1,23) UA = {1, 4,9} ‘A number is randomly selected from set A above, and then a second number is randomly selected ffom set B. What is the probability that the product of che cwo numbers selected will be less than 9? S36 88 8 AIM CINUINGIMw =17. A target shown in the accompanying diagram consists of three circles with the same center. The radii of the circles are 3, 7, and 9. A dare is thrown and lands on the target. What is the probability that the dart will land on the shaded region? 4 ay 4 (a) 3 40 p) 40 @) a 49 © fal (Dp) 2 (D) id 40 On . The six faces of a cube arc numbered 1 through 6. If the cube will be rolled twice in succession, what is the probability that the number that faces up on the first roll will be greater than the number that faces up on the second roll? @) ain In the accompanying diagram, points 4, B, Gand Dare the centers of four circles that cach have a radius length of 1-The circles are tangent at the points shown. If a point is selected at random from the interior of square ABCD, what is.the prob- ability that the will be chosen from the shaded region? 5 @i-% 4 @) 1-32 16, wor 6 D)1-= 1-5 @i-= 16ap LITT In the accompanying diagram, circle Pis inscribed in a square. Ifa point is picked at random from the interior of the square, what is the probability that the point will lie in the shaded region? J M In the accompanying figure, JKLM isa square with sides of length 6. Points‘ and Bare the midpoints of sides KLand LM, respectively. Ifa point is selected at random from the interior of the square, what is the probability chat the point will be chosen from the interior of A/AB? a 2 (8) + oz @?2 1 ( = 220. 21 22. 23. 24, 2s, 26. 27. 28. 29, Adie is rolled once the probability of obtaininga number more than one is Ad 1/6 B)5/6 1/3 D) 2/3 ) None of these A dieis rolled once, the probability of obtaining a number less than 1 is Ay13 Bo o1 d) 2/3 E)1/6 A die is rolled once, the probability of obtaining an integer is ayo B) 1/3 €) 3/5 D)1/6 51 Two dice rolled once, the probability of obtaining same faces is A)1/6 B)O 5/6 Dw £)1/3 Two dice are rolled once, the probability of obtaining an event the sum of digit is 9 Ay1/9 B)O 5/6 D)% 51/3 ‘Two dice are rolled once, the probability of obtaining an event in which one is obtained on one die and other is a multiple of 2 is A) 5/6 B)O 01/6 D)% 51/3 ‘Two dice are rolled once, the probability of ‘obtaining a multiple of three as a product of both events A)S/6 B)O 5/3 b) 11/18 E) None of these Three dice are rolled at once what is probability of obtai a ot i A OF Ds Three dice are rolled once what is the probability that sum of digits is 8 Ne BZ os Ds A coin is tossed once, the probability of obtaining a headis As ay co DM E) None of these 30. A coinis tossed on: ‘no tall" fs, DY oo Dm E) None ofthese ce, the probability of obtaining 31. Acoinis toss headands wane the probability of obtaining a y% on ne . Do E) None ofthese 32. Two coins are tossed to orobeaimas eae together once the probaly ayiya 4 3% O% Da 2% - 33. Two coins are tossed together once, the probabil ofobaininglessthantwoheadsis Ay% 3)% O%* D1 E) None ofthese CaA\Y 34. Two coins are tossed together once, the probability of obtaining more than one tal ay% a Ba Q% alé D)1 E) None of these 35. Two coins are tossed together once, the probability of obtaining at least one head is A) B)1 Ou D)% E) None of these 36. Two coins are tossed together once, the probability of obtaining at most two tails is AY Bt Ow D)% E) None of these 37. Three coins are tossed simultaneously, the probability of obtaining no head is A)1/8 B)1/6 O13 D)% E)% the 38, Three coins are tossed simultaneously, probability of obtaining less than three tails B)1/8 ae 3a E)1 aneously, the 39. Three coins ae essed simultaneously probability of obtaining more 3)1/8 ay1 Ow De E12 ttaneously, the 40, Three coins are tossed simultaneous probability of obtaining at By’ ayo 1 Ow Dd) E7841. 42. 43. ‘Three coins are tossed simultaneously, the probability of obtaining at most three heads is ayt Bo O* D)% E% A die is rolled once, the probability of obtaining an ‘even number ora prime number is ayy B)2/3 OM D)1 E)5/6 A die is rolled once, the probability of obtaining an even number or andpdd number is “A)1/6 B)2/3 Ow D)1/3 E)1 44. 45. 46. 47. 48: 49. Adie is rolled once, the probability of obtaining an ‘odd number or a composite number is Ay1/6 8)1/3 oO D)5/6 2/3 Accoinis tossed once, the probability of obtaining a head or atail is AUG B)1/3 oa D)2/3 51/2 Two dice are rolled once, the probability of obtaining a multiple of three or a sum of ten is Ae 8) 2/3 01/6 bjt 7/12 ‘The probability that Rehan will be able to solve a certain problem is 1/5. That Sohaib will be able to solve is 1/4. Ifboth boys work separately on the problem, the probability that both will solve tis A)1/10 B)1/5 O% D)1/20 Et In awar against terrorism. Jet plane A hit the target 3 times in 5 shots, Jet Plane B hit the target 2 times in 5 shots and jet Plane C hit the target 3 times in 4 shots. fall the planes hit the target independently the probability that they all three hit the target is A) 47/100 B) 19/100 gizy7 ) 9/50 51/50 If the probability that Saima will be alive in 30 years is 4/10 and the probability that Sana will be alive in 30 years in 8/10. The probability that both will be alive in 30 years is A022 8) 0.26 030 D)032 E) 0.40 50. si. 605 52. 53. 54, 55. 56. 57. ‘The probability that Moona will solve a certain matrimonial problem is 1/2. And Farah will solve the same matrimonial problem is 1/4. The probability that Farah will solve certain matrimoniay problem but Moona will not is: AN BM oasi2 byt E18 ‘The probability that a person A will be alive 15 year hence is and the probability that another person 8 will be alive 15 years hence isz. Find the probability that both will be alive 15 year hence. 3 Aas BS D) None of these 2 IFP(A) ='1/2, P(B) = 1/4 and P(A B) the value of P(A UB) Is “ Ay1/B 8) 3/8 ose 78 Bi 7 1 P(A) = 1/3, P(@) ='1/3 and P(A MB) = 1/9 then PAL BY'is ( As BY 2/4 4/9 , 03/7 51/9 For an independent event P(A) = ¥2, P(B) = 1/3 and then P(A B') is Ay 1/8 B)1/9 2/9 D)4/9 E)1/3 For and independent event P(A) = 1/2, P(B) = 1/2, then P(A’ B) is az Bo O% bya E)1/3 IfA and B are events such that P (A)= 0.42, P(B) = 0.48 and P(AVB) = 0.16 then P(A U B) is equal to A)09 B) 0.74 0.2016 D) None ofthese IEP (A) = 0.4, P (B)= p, P (AUB) = 0.6 and A, Bare siven to be independent events, then p= a Be OF D) None of these From a bag containing 4 white and black balls a man draws 3 at random. What is the chance of drawing 3 black balls? A 5/42 B) 16/19 Oia Bal Da Anurn contains 3 white and 5 blac white k balls, One ball is drawn. What is the probability that it is black? % 1/8 B)s/e 6/8 7, a6 D)7/860. 61. 62. 63. 64. 65. 66. 67. 68, _ngroup consists of 4 boys and 3 girs. Thre Ag’elected at random. Find the escume ae Ge the three selected are boys atal Ayay35 o1/ét £) 4/53 Four persons are chosen at random froma group roataining 3 men, 2 women and 4 children. What is the chance that exactly two of them will be children Bya/7 by9y71 46/2 8) 9/57 ©) 4/65 D) 7/42, F) 10/21 From a group of 2 ladies and 3 gents a committee of J pembers is to be formed, The probability that the mittee will consist of 2 gents and 1 lady is com ai 8) 4/5 2/5 »)3/8 51/5 ‘qwo cards are drawn at random from a well-shuffled pack of 52. Find the chance of drawing two aces. 4) 1/200 B) 1/221 1/6 D) 11/16 ) 101/400 ? one card is selected at random froma well-shuffled deck of 52 cards. Find the probability that the card is a7oraclub. Ay4/13 B) 10/17 c9/1sz D) 16/163 1 Inthe draw ofa card from a deck of ordinary playing cards, find the probability that it is either a queen or aheart A) 4/13 B) 5/26 ©) 6/27 D) 5/6 E)7/12 ne cardis selected at random froma well shuffled deck of 52 playing cards. The probability thatthe card is Diamond or a Spade is AK B) 1/52 9 13/82 D) 16/52 Hs One card is selected atrandom froma well shuffled deck of 52 playing cards. The probability that Ll card is jack ora King is Al B)4/17 09/29 ) 6/65 82/13 Abag contains 7 white, § black and 4 red balls. Fw 1m the bag, the me color Is balls are drawn at random fro probability that they are not of the sa 3 yz B ‘Two cards are drawn at random without replacement. The probability that the first is king and second Is nota king is D) None of these A person's chance of winding raf is If he holds 10 tickets, how many tickets have been sold? A) 340 B) 360 120 D)720