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Binomial Distribution · CAPE Applied Mathematics Unit 1

65 past-paper questions on Binomial Distribution, part of Module 2: Managing Uncertainty, from every CAPE Applied Mathematics Unit 1 paper on Quelpr.

Practise Binomial Distribution
  1. 4(c)(i)7 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2Calculate the probability that at least 1 of these 7 bottles contains more than 99.8 ml of pepper sauce.
  2. 4(c)(ii)7 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2Determine the expected number of these 7 bottles that contain more than 101 ml of pepper sauce.
  3. 3(a)(ii)b)3 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Determine the probability that exactly two of the three candles selected are red.
  4. 4(a)3 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2State THREE conditions required for a random variable to follow a binomial distribution.
  5. 4(b)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2State with reason whether drawing three discs with replacement from a bag containing 4 yellow, 3 blue, and 2 white discs can be modelled by a binomial distribution.
  6. 4(b)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2State with reason whether drawing three discs without replacement from a bag containing 5 yellow and 4 blue discs can be modelled by a binomial distribution.
  7. 4(b)(iii)2 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2State with reason whether drawing three discs with replacement from a bag containing 5 yellow and 4 blue discs can be modelled by a binomial distribution.
  8. 4(c)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2For a group of 40 potential donors, calculate the expected number turned away due to tattoos.
  9. 4(c)(ii)a)3 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2For a random sample of 7 prospective donors, calculate the probability that none of them have tattoos.
  10. 4(c)(ii)b)3 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2For a random sample of 7 prospective donors, calculate the probability that exactly 3 of them have tattoos.
  11. 4(c)(ii)c)2 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2For a random sample of 7 prospective donors, calculate the probability that at least one of them has tattoos.
  12. 4(a)(i)1 mark· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2A card is taken from an ordinary pack of cards, its suite (Ace, Spade, Diamond, Heart) noted, and it is replaced in the pack. The process is repeated 12 times. X is the number of spades that were examined.
  13. 4(a)(ii)1 mark· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2A fair die is tossed. This process is repeated a number of times. X is the number of throws of the fair die until a 6 is obtained.
  14. 4(a)(iii)1 mark· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 210 seeds are planted. The probability of a seed germinating is 0.8. X is the number of seeds that germinate.
  15. 4(a)(iv)1 mark· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2A bag contains 8 white and 12 red marbles, all identical except for colour. A marble is taken from the bag and placed in another bag. This process is done 6 times. X is the number of red marbles taken.
  16. 4(b)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2Determine the expected number of patients in the sample who would not keep their follow-up appointment.
  17. 4(b)(ii)a)3 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2Calculate the probability that exactly 4 patients did not keep the follow-up appointment.
  18. 4(b)(ii)b)3 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2Calculate the probability that at most 2 patients did not keep their follow-up appointment.
  19. 4(a)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2How many days in September is it expected to rain?
  20. 4(a)(ii)4 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2What is the probability that it will rain on exactly 3 days in the next 7 days?
  21. 4(b)(i)3 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2Show that n = 15.
  22. 4(b)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2Hence calculate E(Y).
  23. 4(b)(iii)3 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2Calculate P(Y = 10).
  24. 3(a)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Calculate the probability that the number of matches won is EXACTLY two.
  25. 3(a)(ii)3 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Calculate the probability that the number of matches won is at LEAST four.
  26. 3(b)2 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Determine the mean number of matches won.
  27. 4(a)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2State the distribution and its parameters for which X can be modelled.
  28. 4(a)(ii)a)3 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2Calculate the probability that exactly THREE customers pay with cash for their petrol.
  29. 4(a)(ii)b)2 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2Calculate the probability that at least ONE customer pays with cash.
  30. 4(a)(iii)2 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2If 40 persons buy petrol, determine the number of them that are expected to pay with cash.
  31. 4(c)(i)3 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2What is the probability that he sells exactly 3 defective tyres in the next 10 tyres of that brand?
  32. 4(c)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2The supplier expects a shipment of 500 tyres of that brand. How many of these tyres will be expected to be defective?
  33. Q191 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1If X is a random variable with distribution \text{Bin}(n, 0.4) such that \text{E}(X) = 30, then n =
  34. Q231 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1Which of the following statements is NOT a condition for the binomial model of probability?
  35. Q291 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1It is estimated that about 30\% of the population of a country holds university degrees. If 10 citizens of this country are drawn at random, the probability that at least one of them holds a university degree is…
  36. 4(a)3 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2State three conditions necessary to model a variable using a binomial distribution.
  37. 4(b)(i)3 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2Calculate P(X = 3).
  38. 4(b)(ii)4 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2Calculate P(X >= 2).
  39. 4(d)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2Find the expected number of germinating seeds in the package.
  40. 4(d)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2Find the standard deviation of the number of seeds that will germinate.
  41. Q171 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2015 · Paper 1A football team has a \frac{3}{5} probability of winning whenever it plays. If the team plays 8 games, the probability of winning exactly 5 games is
  42. Q301 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2015 · Paper 1In a certain district, it is believed that 60 per cent of the houses are insured against fire. If 140 houses are in the district then the number of houses expected to be insured against fire is
  43. 4(b)(i)3 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Name the distribution of Y, and state its parameters.
  44. 4(b)(ii)a)3 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Calculate the probability that at any moment EXACTLY 4 lines will be engaged.
  45. 4(b)(ii)b)3 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Calculate the probability that at any moment AT LEAST 1 line will be engaged.
  46. Q211 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1A binomial distribution, \text{Bin}(n, p) has n = 250 and p = 0.6. The mean and the variance of this distribution are
  47. Q291 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1It is estimated that about 30% of the population of a country holds university degrees. If 10 citizens of this country are drawn at random, the probability that at least one of them holds a university degree is…
  48. 4(d)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2016 · Paper 2If 80 persons are introduced to the product, determine the number of persons who are expected to buy the product.
  49. 4(d)(ii)3 marks· CAPE Applied Mathematics Unit 1 · 2016 · Paper 2From a random sample of 15 persons who were introduced to the product, calculate the probability that exactly 9 will buy the product.
  50. Q171 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1A football team has a \frac{3}{5} probability of winning whenever it plays. If the team plays 8 games, the probability of winning exactly 5 games is
  51. Q191 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1If X is a random variable with distribution \text{Bin}(n, 0.4) such that E(X) = 30, then n =
  52. Q221 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1Items 22--23 refer to the following information. Ten per cent of bulbs produced by a factory are defective. A sample of 400 bulbs is taken. The mean number of defective bulbs is
  53. Q231 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1Items 22--23 refer to the following information. Ten per cent of bulbs produced by a factory are defective. A sample of 400 bulbs is taken. The variance for the distribution of defective bulbs is
  54. Q281 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1A courier service team has a \frac{3}{5} probability of completing its assigned deliveries in a day. If the team is assigned 8 deliveries on Wednesday, the probability of making exactly 5 deliveries, to 2 decimal…
  55. Q291 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1It is estimated that about 30\% of the population of a country holds university degrees. If 10 citizens of this country are drawn at random, the probability that at least one of them holds a university degree is…
  56. 4(c)(i)4 marks· CAPE Applied Mathematics Unit 1 · 2017 · Paper 2State FOUR assumptions that are made in applying a binomial model to this experiment.
  57. 4(c)(ii)1 mark· CAPE Applied Mathematics Unit 1 · 2017 · Paper 2State a binomial distribution that will model this experiment.
  58. 4(c)(iii)2 marks· CAPE Applied Mathematics Unit 1 · 2017 · Paper 2What is the probability that exactly 4 seedlings will NOT survive transplantation?
  59. 4(a)(i)1 mark· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Identify the distribution that may be used to model this situation.
  60. 4(a)(ii)1 mark· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2State the parameters of the distribution.
  61. 4(a)(iii)2 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Determine the expected number of customers in the sample who do not make their monthly payments on time.
  62. 4(a)(iv)2 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Calculate the probability that exactly 5 customers do not make their monthly payments on time.
  63. 4(a)(v)4 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Calculate the probability that at most 3 customers do not make their monthly payments on time.
  64. 4(a)(i)3 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Determine the probability of getting at LEAST nine of the intended numbers when ten independent calls are made.
  65. 4(a)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Calculate the mean number of intended numbers and the variance when ten independent calls are made.

Related topics in Module 2: Managing Uncertainty