Tiêu đề XII - maths - chapter 11 - PROBABILITY (93-113).pdf ✅

93 PROBABILITY NARAYANAGROUP SR.MATH-2A - MAIN VOL-II PROBLEMS ON CLASSICAL DEFINITION OF PROBABILITY 1. A positive integer is selected at random. If A be the event that it is divisible by 5 and B be the event that it has zero at the units place, then A B  is 1) An impossible event 2) a certain event 3) A B  4) the event that the number has a non-zero digits at the units place 2. There are 7 seats in a row. Three persons take seats at random the probability that the middle seat is always occupied and no two persons are consecutive is 1) 9 70 2) 9 35 3) 4 35 4) 6 35 3. If the letters of the word MISSISSIPPI are arranged at random, the probability that all the 4 S's appear consecutively is 1) 8 11   2) 4 11   3) 8 4 11    4) 6 11   4. If 10 persons are to sit around a round table, the odds against two specified persons sitting together is 1) 1 9 2) 2 9 3) 7 to 2 4) 2 to 7 5. The probability that the birthdays of 6 girls will fall on 6 different calender months of a year is 1) 5 1 12 2) 6 6 6 12 c 3) 12 6 6 12 p 4) 11 1 12 6. Out of numbers 1 to 9, two numbers are chosen at random, so that their sum is even number. The probability that the two chosen numbers are odd is 1) 5 18 2) 13 18 3) 5 8 4) 1 8 7. Three integers are chosen at random without replacement from the 1st 20 integers. The probability that their product is odd is 1) 3 19 2) 2 19 3) 1 19 4) 4 19 8. There are m persons sitting in a row. Two of them are selected at random. The probability that the two selected persons are together 1) 1 2 2 m m c c  2) 2 1 m m c  3) 2 3 m m c  4) 1 2 2 1 m m c c   9. Consider a lottery that sells 2 n tickets and awards n prizes. If one buys n tickets the probability of his winning is i.e., getting at least one prize is 1) 2 n n n c 2)   2 1 2 n n n n n c c   3)   2 2 n n n  4) 2 1 n n c 10. Dialling a telephone number to his daughter an old man forgets the last two digits and dialled at random remembering only that they are different. The probability that the number dialled is correct is 1) 1 10 2) 1 45 3) 1 90 4) 1 135 11. 12 balls are distributed among 3 boxes. The probability that the 1st box contains 3 balls is 1) 10 2 3       2) 10 100 9 3  3) 10 110 2 9 3       4) 100 9 12. Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all three apply for the same house is 1) 1/9 2) 2/9 3) 7/9 4) 8/9 13. There are 2 locks on the door and the keys are among the six different ones you carry in your pocket. In a hurry you dropped one somewhere. The probability that you can still open the door is 1) 1 2 2) 1 3 3) 2 3 4) 1 4 14. Two friends A and B have equal number of sons. There are 3 cinema tickets which are to be distributed among the sons of A and B. The probability that all the tickets go to sons of B is 1/20. The number of sons, each of them having is 1) 2 2) 4 3) 5 4) 3 15. Three groups of children contain respectively 3 girls & 1 boy; 2 girls & 2 boys; 1 girl & 3 boys. One child is selected at random from each group. The chance that the three selected children consists of one girl and 2 boys is 1) 9 32 2) 11 32 3) 13 32 4) 7 32 LEVEL-II (C.W)
94 PROBABILITY NARAYANAGROUP SR.MATH-2A - MAIN VOL-II 16. A letter is taken out at random from the word ASSISTANT and an other from STATISTICS. The probability that they are the same letters is 1) 13 90 2) 17 90 3) 19 90 4) 15 90 17. If a number x is selected from the 1st 100 natural numbers at random, then the probability that 100 x 50 x   is 1) 9 20 2) 1 2 3) 11 20 4) 5 20 18. Three newly wedded couples are dancing at a function. If the partner is selected at random the chance that all the husbands are not dancing with their own wives is 1) 1 3 2) 1 6 3) 5 6 4) 2 3 19. 2n boys are randomly divided into two subgroups containing n boys each. The probability that the two tallest boys are in different groups is 1) 1 2 2) n 2n 1 3)     n 1 2n 1   4) 2n 2n 1 20. A bag contains apples and oranges, five in all and atleast one of each, all combinations being equally likely. If one fruit is selected at random from the bag, assuming all fruits are distinguishable, the probability that it is an orange is 1) 1 20 2) 1 10 3) 1 5 4) 1 2 21. There are 10 stations between A and B. A train is to stop at three of these 10 stations. The probability that no two of these stations are consecutive is 1) 8 3 10 3 c c 2) 9 3 10 3 c c 3) 7 3 10 3 c c 4) 10 3 12 3 c c 22. If the papers of 4 students can be checked by any one of the seven teachers then the probability that all the four papers are checked by exactly two teachers is 1) 6 49 2) 2 7 3) 32 343 4) 2 343 23. A box contains 100 tickets numbered 1, 2, ...., 100. Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than 10. The probability that the minimum number on them is 5 is 1) 1 9 2) 2 9 3) 3 9 4) 4 9 24. Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is 1) 3 5 2) 1 5 3) 2 5 4) 4 5 25. Two integers x and y are chosen with replacement out of the set 0, 1, 2, 3, ......,10 . Then the probability that x y 5   is 1) 81 121 2) 30 121 3) 25 121 4) 20 121 26. A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant is positive is 1) 3 16 2) 3 8 3) 5 8 4) 7 8 27. A team of 8 couples (husband and wife) attend a lucky draw in which 4 persons picked up for a prize. Then the probability that there is atleast one couple is 1) 11 39 2) 12 39 3) 14 39 4) 15 39 28. A subset A of X = {1, 2, 3, ...., 100} is chosen at random. The set X is reconstructed by replacing the elements of A and another subset B of X is chosen at random. The probability that A B  contains exactly 10 elements is 1) 1 10 2) 100 100 10 1 2 c       3) 100 100 10 1 4 c       4) 90 100 10 100 3 4 c 29. A has 3 tickets of a lottery containing 3 prizes and 9 blanks. B has two tickets of another lottery containing 2 prizes and 6 blanks. The ratio of their chances of success is 1) 32 15 : 55 28 2) 32 13 : 55 28 3) 34 13 : 55 28 4) 34 15 : 55 28
95 PROBABILITY NARAYANAGROUP SR.MATH-2A - MAIN VOL-II 30. S = {1, 2, 3, ..... 11} if 3 numbers are chosen at random from S, the probability for they are in G.P. 1) 11 3 7 c 2) 11 3 9 c 3) 11 3 5 c 4) 11 3 4 c 31. If 10 identical apples are distributed among 6 persons at random then the probability that atleast one of them will receive none is 1) 6 143 2) 14 4 15 5 c c 3) 137 143 4) 1 143 32. In a game called ‘odd man out’, 4 persons toss a coin to decide who will buy refreshments for the entire group. A person who gets an outcome different from that of the rest of the members of the group is called the odd man out. The probability that there is a loser in any game is 1) 1/3 2) 1/4 3) 1/2 4) 1/5 33. Two numbers ‘a’ and ‘b’ are chosen at random from the numbers 1,2,3,....30. The chance that a2 – b2 is divisible by ‘3’ is 1) 9 87 2) 12 87 3) 15 87 4) 47 87 34. Two numbers are selected at random from 1,2,3,.....,100 and are multiplied, then the probability that the product thus obtained is divisible by 3 correct to two places of decimal is 1) 0.45 2) 0.55 3) 0.25 4) 0.35 35. Four digit numbers with different digits are formed using the digits 1,2,3,4,5,6,7,8. One number from them is picked up at random. The chance that the selected number contains the digit ’1’ is 1) 1 2 2) 1 4 3). 1 8 4) 1 16 36. Three numbers are chosen at random from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The probability that the smallest of the three numbers chosen is even is 1) 5 12 2) 7 12 3) 5 6 4) 1 6 37. Out of 5 digits 0, 3, 3, 4, 5 five digit numbers are formed. If one number is selected at random out of them. The probability that it is divisible by 5 is 1) 3 16 2) 5 16 3) 7 16 4) 9 16 38. From the first 100 natural numbers a number is chosen at random, the probability for it to be a composite number is 1) 74 100 2) 24 100 3) 25 100 4) 26 100 39. From 101 to 1000 natural numbers a number is taken at random. The probability that the number is divisible by 17 is 1) 58 900 2) 58 100 3) 53 900 4) 53 1000 40. 3 coins are marked with a, b; b,c; c,a. All are tossed, probability that two of the faces shows the same letter is 1) 3 8 2) 1 8 3) 3 4 4) 1 4 41. A magical die is so loaded that the probability of any face appearing is proportional to the number of points on its face. The probability of an odd number appearing is 1) 2 7 2) 3 7 3) 4 7 4) 5 7 42. A die is loaded such that 6 turning upwards is twice as often as 1 and three times as any other face. The chance that we get a face with one point when we throw such a die is 1) 6 17 2) 3 17 3) 2 17 4) 5 17 43. A fair die is thrown untill a face with less than 5 points is obtained. The probability of obtaining not less than 2 points on the last throw is 1) 1 4 2) 1 2 3) 3 4 4) 1 8 44. An ordinary die has four blank faces. One face marked 2, an other marked 3) Then the probability of obtaining a total of exactly 12 in 5 throws is 1) 4 15 6 2) 4 10 6 3) 4 5 6 4) 4 6 6 45. A and B throw a symmetrical die each. The odds against ‘ A’ not throwing a number greater than B is 1) 1 to 5 2) 5 to 1 3) 7 to 5 4) 5 to 7
96 PROBABILITY NARAYANAGROUP SR.MATH-2A - MAIN VOL-II 46. Three faces of a fair die are yellow, two faces red and one blue. The die is thrown twice. The probability that 1st throw will give an yellow face and the second a blue face is 1) 1 6 2) 1 9 3) 1 12 4) 1 3 47. In a single throw with a pair of dice, the total score of occurrence for which the probability is maximum is 1) 5 2) 6 3) 7 4) 8 48. If three dice are thrown, then the probability that they show the numbers in A.P. is 1) 1 36 2) 1 18 3) 2 9 4) 5 18 49. It is given that there are 52 Thursdays in a leap year. Then the probability that it will have 52 Fridays is 1) 2 5 2) 4 5 3) 1 5 4) 3 5 50. Two children were picked at random and found to have been born in 1992 then the probability that exactly one of them is born on 29th February is 1) 0 2) 1 366 183  3) 365 366 183  4) 2 731 (366) 51. Five cards are drawn at random from a well shuffled pack of 52 playing cards. The probability that four of them may have the same face value is 1) 13 4 48 1 1 1 52 5 c c c c   2) 13 48 1 1 52 5 c c c  3) 13 5 52 5 c c 4) 13 4 4 1 52 5 c c c  52. The probability of getting 9 cards of the same suit by a particular hand at a game of bridge is 1) 13 9 52 13 c c 2) 13 39 9 4 52 13 c c c  3) 4 13 39 1 9 4 52 13 c c c c   4) 4 13 1 9 52 13 c c c  53. In a hand at which the probability that 4 queens are held by a specified player is 1) 48 9 52 13 4 c c  2) 48 9 52 13 c c 3) 48 13 52 13 4 c c  4) 48 13 52 13 2 c c  54. Two cards drawn one after another at random without replacement. The probability that both of them may have the same face value is 1) 1 221 2) 1 169 3) 1 17 4) 1 19 55. Two cards are drawn at random from a pack of 52 cards. The probability of getting atleast a spade and an ace is 1) 1 34 2) 8 221 3) 1 26 4) 2 51 56. The probability of getting different suit cards and different denomination cards when two cards are drawn from a pack is 1) 13 17 2) 13 34 3) 12 17 4) 6 17 57. There are 3 cards. Each is painted red on one side and black on the other side. The cards are randomly placed in a row. The probability that no two consecutive cards show red is 1) 3 8 2) 5 8 3) 5 6 4) 1 8 58. A bag contains 10 white and 3 black balls. Balls are drawn one by one without replacement till all the black balls are drawn. The probability that the test will come to an end at the 7th draw is 1) 4 2 6 10 3 1 13 7 c c c   2) 4 2 6 10 3 2 13 7 c c c   3) 4 2 7 10 3 13 c c c  4) 5 2 7 10 3 13 c c c  59. Four tickets numbered 00, 01, 10, 11 are placed in a bag. A ticket is drawn at random and replaced. Again a ticket is drawn at random. The probability that the sum of the numbers on the tickets drawn is 21 1) 1 4 2) 1 8 3) 1 16 4) 1 12 60. Two squares of a chess board having 8 8  squares are selected at random the probability that they have a side in common is 1) 64 2 56 c 2) 64 2 112 c 3) 64 2 168 c 4) 64 2 268 c