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Counting · CAPE Pure Mathematics Unit 2

113 past-paper questions on Counting, part of Counting, Matrices and Differential Equations, from every CAPE Pure Mathematics Unit 2 paper on Quelpr.

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  1. 5(a)(i)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2005 · Paper 2Copy and complete the diagram to represent the event space.
  2. 5(a)(ii)a)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2005 · Paper 2Find the probability that a customer chosen at random who had purchased premium gasoline requested a check for engine oil.
  3. 5(a)(ii)b)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2005 · Paper 2Find the probability that a customer chosen at random who had requested a check of the brake fluid purchased regular gasoline.
  4. 5(a)(ii)c)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2005 · Paper 2Find the probability that a customer chosen at random who had requested a check of the engine oil purchased regular gasoline.
  5. 5(b)(i)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2005 · Paper 2Calculate the total number of ways of choosing the three balls.
  6. 5(b)(ii)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2005 · Paper 2Calculate the probability that ONE ball of EACH colour is drawn.
  7. 5(b)(iii)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2005 · Paper 2Calculate the probability that ALL THREE balls drawn are of the SAME colour.
  8. 5(a)(i)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2006 · Paper 2How many numbers lying between 3 000 and 6 000 can be formed from the digits, 1, 2, 3, 4, 5, 6, if no digit is used more than once in forming the number?
  9. 5(a)(ii)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2006 · Paper 2Determine the probability that a number in 5(a)(i) above is even.
  10. 5(a)(i)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2Determine the number of ways of selecting the six marbles if there are no restrictions.
  11. 5(a)(ii)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2Find the probability that the marbles chosen contain more black marbles than white marbles.
  12. 5(b)(i)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2Determine the probability that a person selected at random is a female.
  13. 5(b)(ii)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2Determine the probability that a person selected at random is a male or likes watching the News.
  14. 5(b)(iii)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2Determine the probability that a person selected at random is a female that likes watching Friends.
  15. 5(b)(iv)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2Determine the probability that a person selected at random does not like watching Matlock.
  16. 5(a)(i)8 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (Rest of Region) · Paper 2In how many ways can this committee be selected so that the committee includes AT LEAST ONE former batsman?
  17. 5(a)(ii)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (Rest of Region) · Paper 2In how many ways can this committee be selected so that the committee includes AT LEAST ONE batsman and ONE bowler?
  18. 5(a)(i)a)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (T&T) · Paper 2How many 4-digit numbers can be formed if the digits 1, 2, 3, 4, 7, 9 can all be repeated?
  19. 5(a)(i)b)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (T&T) · Paper 2How many 4-digit numbers can be formed if none of the digits 1, 2, 3, 4, 7, 9 can be repeated?
  20. 5(a)(ii)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (T&T) · Paper 2Calculate the probability that a 4-digit number formed without repetition is even.
  21. 5(b)6 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (T&T) · Paper 2A father and son practise shooting at basketball, and score when the ball hits the basket. The son scores 75\% of the time and the father scores 4 out of 7 tries. If EACH takes one shot at the basket, calculate…
  22. 5(a)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2009 · Paper 2A committee of 4 persons is to be chosen from 8 persons, including Mr Smith and his wife. Mr Smith will not join the committee without his wife, but his wife will join the committee without him. Calculate the number of…
  23. 5(b)(i)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2009 · Paper 2the numbers on BOTH balls are even
  24. 5(b)(ii)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2009 · Paper 2the number on one ball is odd and the number on the other ball is even.
  25. 5(a)(i)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2010 · Paper 2Calculate the number of different permutations of the 8 letters of the word SYLLABUS.
  26. 5(a)(ii)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2010 · Paper 2Calculate the number of different selections of 5 letters which can be made from the letters of the word SYLLABUS.
  27. 5(b)(i)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2010 · Paper 2Find P(A \cap B).
  28. 5(b)(ii)a)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2010 · Paper 2Stating a reason, determine whether or not the events A and B are mutually exclusive.
  29. 5(b)(ii)b)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2010 · Paper 2Stating a reason, determine whether or not the events A and B are independent.
  30. 5(b)(i)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2011 · Paper 2Find the number of 5-digit numbers greater than 30 000 which can be formed with the digits, 1, 3, 5, 6 and 8, if no digit is repeated.
  31. 5(b)(ii)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2011 · Paper 2What is the probability of one of the numbers chosen in (b)(i) being even?
  32. 5(a)(i)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2012 · Paper 2Determine how many such numbers can be formed if each digit appears at most once.
  33. 5(a)(ii)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2012 · Paper 2Determine how many such numbers can be formed if there is no restriction on the number of times a digit may appear.
  34. 5(b)(i)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2012 · Paper 2Find the probability that the committee consists entirely of Jamaicans.
  35. 5(b)(ii)6 marks· CAPE Pure Mathematics Unit 2 · May/June 2012 · Paper 2Find the number of ways in which the committee can be formed, given the restriction that there are as many Tobagonians on the committee as there are Guyanese.
  36. 5(a)7 marks· CAPE Pure Mathematics Unit 2 · May/June 2013 · Paper 2Three letters from the word BRIDGE are selected one after the other without replacement. When a letter is selected, it is classified as either a vowel (V) or a consonant (C). Use a tree diagram to show the possible…
  37. 5(c)(i)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2013 · Paper 2A country, X, has three airports (A, B, C). The percentage of travellers that use each of the airports is 45\%, 30\% and 25\% respectively. Given that a traveller has a weapon in his/her possession, the…
  38. 5(c)(ii)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2013 · Paper 2On a particular day, a traveller was caught carrying a weapon at an airport in Country X. What is the probability that the traveller used airport C?
  39. 5(a)(i)7 marks· CAPE Pure Mathematics Unit 2 · May/June 2014 · Paper 2Five teams are to meet at a round table. Each team consists of two members AND one leader. How many seating arrangements are possible if each team sits together with the leader of the team in the middle?
  40. 5(a)(ii)a)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2014 · Paper 2Given that 40% of the individuals used red and 50% used blue, calculate the probability that an individual used BOTH colours.
  41. 5(a)(ii)b)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2014 · Paper 2Determine the TOTAL number of individuals that participated in the experiment.
  42. Q311 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 1In how many ways can the letters ABCDE be arranged so that the A and B are always together?
  43. Q321 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 1The number of distinct permutations of the letters of the word POSSIBILITY is
  44. Q331 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 1A relay team of five teachers is to be chosen from a group of 15 teachers. In how many ways could this relay team be chosen?
  45. Q341 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 1X and Y are mutually exclusive events. If P(X) = \frac{1}{4} and P(Y) = \frac{1}{5}, then P(X \cup Y) =
  46. Q391 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 1The letters of the word I R R E G U L A R are to be arranged in a line. The number of possible arrangements in which the 3 Rs are NOT together is
  47. Q401 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 1Two coins and a die with faces numbered 1 to 6 are thrown together once. Assuming that the die and coins are fair, the probability of obtaining 2 heads and a number less than 4 is
  48. 5(a)(i)1 mark· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 2Determine the number of possible ways in which a group of FOUR applicants may be selected if no restrictions are applied.
  49. 5(a)(ii)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 2Determine the number of possible ways in which a group of FOUR applicants may be selected if at least one of the successful applicants must be female.
  50. 5(b)(i)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 2Determine the greatest possible amount of numbers that may be formed.
  51. 5(b)(ii)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 2Determine the probability that a number formed is greater than 100.
  52. Q281 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 1A relay team of 5 teachers is to be chosen from a group of 15 teachers. In how many ways could this relay team be chosen?
  53. Q311 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 1In how many ways can the letters P, Q, R, S and T be arranged so that P and Q are always together, and R and S are always together?
  54. Q351 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 1A sample space X consists solely of 3 mutually exclusive events, Q, R and S. If P(Q) = 0.3 and P(R) = 0.6, then P(S) =
  55. Q361 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 1A school debating team comprising 3 teachers, 3 boys and 3 girls is to be chosen from 5 teachers, 4 boys and 6 girls. The number of ways in which this team can be chosen is
  56. Q371 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 1One person is randomly selected. What is the probability that this person is female and prefers Drink B?
  57. Q401 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 1Two coins and a die with faces numbered 1 to 6 are thrown together once. Assuming that the die and coins are fair, the probability of obtaining 2 heads and a number less than 4 is
  58. Q431 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 1The probability that L occurs, given that K occurs, is
  59. 3(c)(i)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2Given that ^n P_r = n! / (n - r)!, show that (^2r P_r * ^n P_r) / ((2r)!) is equal to the binomial coefficient ^n C_r.
  60. 5(a)(i)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2Determine the number of possible seating arrangements of the passengers who boarded the bus at the terminal.
  61. 5(a)(ii)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2At the first stop, no passengers will get off the bus but there are eight other persons waiting to board the same bus. Among those waiting are three friends who must sit together. Determine the number of possible groups…
  62. 5(b)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2What is the probability that Gavin and Alexander are the opening pair for a given match?
  63. 6(a)(i)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2Calculate the number of outcomes in the sample space.
  64. 6(a)(ii)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2Find the probability of obtaining exactly one head.
  65. 6(a)(iii)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2Calculate the probability of obtaining at least one head on the coins and an even number on the die on a particular attempt.
  66. Q311 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 1In how many ways can the letters ABCDE be arranged so that the A and B are always together?
  67. Q331 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 1The probability that L occurs, given that K occurs, is
  68. Q351 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 1A sample space S consists of 3 mutually exclusive and exhaustive events Q, R and S. If P(Q) = 0.3 and P(R) = 0.6, then P(S) =
  69. Q381 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 1The letters of the word IRREGULAR are to be arranged in a line. The number of possible arrangements in which the 3 Rs are NOT together is
  70. Q401 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 1Two coins and a die with faces numbered 1 to 6 are thrown together once. Assuming that the die and coins are fair, the probability of obtaining 2 heads and a number less than 4 is
  71. Q411 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 1A bag contains 6 blue balls and 4 red balls. Terry chooses 2 balls at random from the bag without replacement. The probability that BOTH balls are red is
  72. 4(a)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 2Eight boys and two girls are to be seated on a bench. How many seating arrangements are possible if the girls can neither sit together nor sit at the ends?
  73. 5(a)(i)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 2Given that P(A \cup B) = 0.7, calculate P(A \text{ only}).
  74. 5(a)(ii)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 2Hence, determine whether events A and B are independent. Justify your answer.
  75. 5(b)(i)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 2Represent the outcomes of the draws and their corresponding probabilities on a tree diagram.
  76. 5(b)(ii)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 2Determine the probability that the second ball drawn is white.
  77. Q331 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 1Two coins and a die with faces numbered 1 to 6 are thrown together once. Assuming that the die and coins are fair, the probability of obtaining 2 heads and a number less than 4 is
  78. Q351 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 1If marbles are chosen, without replacement, from a bag of 10 blue and 5 red marbles, then the probability of getting a red marble followed by 2 blue marbles is
  79. Q361 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 1A school debating team comprising 3 teachers, 3 boys and 3 girls is to be chosen from 5 teachers, 4 boys and 6 girls. The number of ways in which this team can be chosen is
  80. Q421 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 1The probability that L occurs, given that K occurs, is
  81. Q431 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 1Chad, Matthew, Josh, Paul and Tifanny are travelling in a five-seater car with 3 persons in the back and 2 persons in the front. Each person occupies a seat. The number of different ways they can sit in the car if…
  82. 5(a)(i)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 2Calculate P(A intersect B).
  83. 5(a)(ii)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 2Determine whether events A and B are independent. Justify your response.
  84. 5(b)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 2A committee of 4 persons is to be chosen from 8 persons, including Mr Smith and his wife. Mr Smith will not join the committee without his wife, but his wife will join the committee without him. Calculate the number of…
  85. 5(c)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 2How many odd numbers greater than 500 000 can be made from the digits 2, 3, 4, 5, 6, 7 without repetitions?
  86. Q321 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2019 · Paper 1From the letters A, B, C, D and E, the number of three-letter words that can be made if no letter is repeated is
  87. Q331 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2019 · Paper 1Item 33 refers to the following Venn diagram which shows the probabilities associated with events K and L in a sample space S. \nThe probability that L occurs, given that K occurs, is
  88. Q341 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2019 · Paper 1A committee of 3 teachers, 3 doctors and 3 lawyers is to be chosen from 5 teachers, 4 doctors and 6 lawyers. The number of ways in which this committee can be chosen is
  89. Q371 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2019 · Paper 1A relay team of 5 teachers is to be chosen from a group of 15 teachers. \nIn how many ways could this relay team be chosen?
  90. 5(a)(i)3 marks· Pure Mathematics · Unit 2 Q5 5(a)(i)Represent the possible outcomes of a single trial of this experiment on a tree diagram.
  91. 5(a)(i)2 marks· Pure Mathematics · Unit 2 Q5 5(a)(i)Determine the sample space of the possible outcomes of the experiment.
  92. 5(a)(i)4 marks· Pure Mathematics · Unit 2 Q5 5(a)(i)How many numbers made up of five digits can be made from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 if each number contains exactly one even digit and no digit is repeated?
  93. 5(a)(ii)4 marks· Pure Mathematics · Unit 2 Q5 5(a)(ii)Determine the probability that the number formed in (a)(i) is less than 30 000.
  94. 5(a)(ii)4 marks· Pure Mathematics · Unit 2 Q5 5(a)(ii)Determine the probability that a golf ball is drawn on the first trial of the experiment.
  95. 5(a)(ii)2 marks· Pure Mathematics · Unit 2 Q5 5(a)(ii)Calculate P(H|F).
  96. 5(a)(iii)3 marks· Pure Mathematics · Unit 2 Q5 5(a)(iii)State, with reason, whether H and F are independent events.
  97. 5(b)4 marks· Pure Mathematics · Unit 2 Q5 5(b)Alex has five blue marbles, four green marbles and three red marbles. In how many ways can he arrange four marbles in a row, if the marbles of any given colour are identical?
  98. 5(b)(i)5 marks· Pure Mathematics · Unit 2 Q5 5(b)(i)In how many ways can the group be seated in the cars if two particular persons refuse to travel in the same car?
  99. 5(b)(i)4 marks· Pure Mathematics · Unit 2 Q5 5(b)(i)Draw a tree diagram to represent the possible events and their respective probabilities.
  100. 5(b)(i)2 marks· Pure Mathematics · Unit 2 Q5 5(b)(i)Calculate the number of ways of arranging 3 letters from the first 6 letters of the alphabet.
  101. 5(b)(ii)5 marks· Pure Mathematics · Unit 2 Q5 5(b)(ii)On a table, there is space for 10 books out of a total of 16 available books. However, a Bible and a book of ghost stories must go at the ends. In how many ways can the books be arranged on the table?
  102. 5(b)(ii)4 marks· Pure Mathematics · Unit 2 Q5 5(b)(ii)Determine the probability that at least one pencil taken from the bag is blue.
  103. 5(b)(ii)3 marks· Pure Mathematics · Unit 2 Q5 5(b)(ii)Calculate the number of ways of arranging ALL the letters of the word SUCCESS.
  104. 5(b)(iii)2 marks· Pure Mathematics · Unit 2 Q5 5(b)(iii)Determine whether the result of the second draw is independent of the first draw. Justify your response.
  105. 5(c)4 marks· Pure Mathematics · Unit 2 Q5 5(c)Let A and B be two events such that P(A) = 1/2, P(B) = 1/4 and P(A ∩ B) = 1/8. Calculate the value of P(A' ∩ B').
  106. 5(c)4 marks· Pure Mathematics · Unit 2 Q5 5(c)Determine in how many ways a sub-committee may be formed if 2 Mathematics teachers and 3 English teachers are selected in no particular order.
  107. 5(c)(i)7 marks· Pure Mathematics · Unit 2 Q5 5(c)(i)In how many different ways can the committee be formed?
  108. 5(c)(i)3 marks· Pure Mathematics · Unit 2 Q5 5(c)(i)Given that 40% of the individuals selected green and 50% selected blue, calculate the probability that an individual selected BOTH colours.
  109. 5(c)(ii)3 marks· Pure Mathematics · Unit 2 Q5 5(c)(ii)What is the probability that the committee formed will contain neither of the 2 men who refuse to serve together?
  110. 5(c)(ii)2 marks· Pure Mathematics · Unit 2 Q5 5(c)(ii)Determine the total number of individuals who participated in the experiment.
  111. 6(a)5 marks· Pure Mathematics · Unit 2 Q6 6(a)A chemical test kit is 95% accurate in detecting when a solution is acidic. However, the test kit also yields a 'false positive' result for 1% of all solutions tested. If 0.5% of the solutions tested are acidic, what is…
  112. 6(a)(i)2 marks· Pure Mathematics · Unit 2 Q6 6(a)(i)Determine P(A|B).
  113. 6(a)(ii)2 marks· Pure Mathematics · Unit 2 Q6 6(a)(ii)Calculate the probability that a member of the population, selected at random, is colour-blind.

Related topics in Counting, Matrices and Differential Equations