Math topic中文

Addition multiplication of probabilities

Addition and multiplication of probabilities.

Practice questions

  1. 1An amateur music composer is arranging a sequence of four musical notes followed by three beats. There are 7 possible no…
  2. 2Two brothers Kai and Leo are duathlon (running and cycling) athletes who train regularly. For each day, the probability…
  3. 3Colour Vision Deficiency is the decreased ability to see differences in colours. Someone with normal colour vision will…
  4. 4A pair of siblings, Abbey and Betty, went to a book fair with six other friends. The eight of them stood in a queue in r…
  5. 5A particular disease is known to infect approximately 1 in every 10 000 people. A test for this disease is 99.9% accurat…
  6. 6A bag contains one green disc, rr red discs and 2r2r blue discs, where r>1r>1. Tim and Sim play a game by taking turns t…
  7. 7Kelly has a box of spherical beads labelled with the 26 letters from A to Z, all of which have the same size. For each l…
  8. 8Happie, the owner of a store selling novelty items, is organizing a publicity stunt for his store. Using a stock of ultr…
  9. 9A fruit seller sources his oranges from a supplier with a large plantation where 1% of the oranges are rotten. The suppl…
  10. 10Tetrahedral dice have four faces. Two fair tetrahedral dice, one red and one blue, have faces numbered 0, 1, 2, and 3 re…
  11. 11By the end of 2022, the percentages of a population who has received V dose(s) of Covid-19 vaccine are shown in the tabl…
  12. 12A circular target board is made up of 3 concentric circles as shown below. The circles have the same centre and their ra…
  13. 13Section B: Statistics [60 marks] Given that events AA and BB are independent, show that A′A' and BB are also independ…
  14. 14A store owner receives a shipment of stationery items, including notebooks, pens, and correction tapes. Historical data…
  15. 15A bag contains 3 red balls and nn yellow balls, where n≥2n \ge 2. In a game, Joe removes 2 balls at random from the bag…
  16. 16For events AA and BB, it is given that P(A)=0.38\mathrm{P}(A) = 0.38, P(A∣B)=0.5\mathrm{P}(A \mid B) = 0.5 and P(A∪B)=0.52\mathrm{P}(A \cup B) = 0.52…
  17. 17The mass, XX grams, of soup packed into a can by machine AA is normally distributed with mean μ\mu grams and standard…
  18. 18Pat is invited to a game show. In the game, she is presented with a box with kk balls with either 1, 2, 3 or 4 printed…
  19. 19The probability of obtaining a head when a particular coin is tossed is pp. A fair cubical die has the number '1' on on…
  20. 20A game is played in which a tetrahedral die is thrown. The sides of the die are numbered 1, 2, 3, 4. Whatever number on…
  21. 21A bakery produces batches of cookies. On average, the proportion of flawed cookies produced is pp, where 0<p<10 < p < 1. T…
  22. 22A nursery supplies plants to Evergreen Pte. Ltd. The heights, in centimetres, of plants supplied may be taken to follow…
  23. 23[For this question, you should state clearly the values of the parameters of any normal distribution you use.] After din…
  24. 24In this question you should state clearly the parameters of any normal distributions you use. The masses in kilograms of…
  25. 25A set of 9 cards are numbered 1, 1, 2, 2, 3, 3, 4, 5 and 6. A round of matching game is played where two cards are drawn…
  26. 26Two families plan to go on a hiking trip together. There are 10 people from the Lee family, consisting of 3 married coup…
  27. 27In a supermarket lucky draw, a participant will first spin a wheel, followed by throwing a fair six-sided die. The wheel…
  28. 28A bag contains 10 red and 15 green beads which are indistinguishable apart from colour. Beads are drawn from the bag sin…
  29. 29A class of twenty-five pupils consists of 15 girls and 10 boys. At the beginning of the year four pupils are to be chose…
  30. 30The diagram below shows a circular target board of radius 40 cm, divided by two concentric circles of radii 12 cm and 24…
  31. 31The diagram below shows a circular target board of radius 40 cm, divided by two concentric circles of radii 12 cm and 24…
  32. 32A policeman inspects each passenger in the car that he stops during a roadblock. The number of passengers in a randomly…
  33. 33Happie, the owner of a store selling novelty items, is organizing a publicity stunt for his store. Using a stock of ultr…
  34. 34Two fair n-sided dice, each with faces numbered 1, 2, ..., n, (where n≥4n \ge 4) are tossed in an experiment. The n…
  35. 35The table below shows the number of male and female students studying Chemistry, Physics and Biology at a private school…
  36. 36At a particular game stall, players throw darts at a target board to earn points for redeeming prizes. The target board…
  37. 37A box contains 1 red, 1 blue and nn yellow discs, where n≥2n \ge 2. Two discs are randomly drawn from the box, without r…
  38. 38A pair of siblings, Abbey and Betty, went to a book fair with six other friends. The eight of them stood in a queue in r…
  39. 39In this question, you should state the parameters of any distribution that you use. A local fish market is famous for tw…
  40. 40A bag contains 4 red counters and 6 blue counters. 4 counters are drawn from the bag at random, without replacement. Cal…
  41. 41At the drinks stall in a canteen, both hot and cold drinks are sold. The number of hot drinks sold per minute follows a…
  42. 42**In this question, you should state clearly all the distributions that you use, together with the values of the appropr…
  43. 43In Sunny Island Republic, all male citizens are required to undergo a National Physical Fitness Assessment (NPFA) Test b…
  44. 44A fair cubical die has faces each labelled with one of the four numbers: 1, 2, 3 and 4. The die is thrown once and the n…
  45. 45A 6-sided die has three faces marked with a '1', two faces marked with a '2' and one face marked with a '3'. Another 6-s…
  46. 46A bag contains four red and eight blue balls of which two of the red balls and six of the blue balls have the number "0"…
  47. 47Serene plays a simple online game which moves a counter one step at a time along a straight line. The counter starts fro…
  48. 48In a game, a player tosses a fair die, whose faces are numbered from 1 to 6. If the player obtains a 6, he tosses the di…
  49. 49Epple Company manufactures a large number of E-phones. It is known that 1% of the E-phones manufactured are defective. A…
  50. 50A code consists of 10 characters. The first 5 characters of the code is formed using 5 letters chosen from the set {A,B,C,D,E,F,G,H}\{A, B, C, D, E, F, G, H\}…
  51. 51An eatery is giving out free burgers in a promotion to celebrate its anniversary. A total of 80 burgers, consisting of 8…
  52. 52A particular disease is known to infect approximately 1 in every 10 000 people. A test for this disease is 99.9% accurat…
  53. 53Students seeking admission to Kingdom University and Island University are required to apply using their national examin…
  54. 54Two digits XX and YY are chosen independently at random from the set of 10 digits {0, 1, 2, . . . , 9}. Events AA and…
  55. 55In each batch of pralines that a chocolate factory produces, they are packed into boxes of 16. Due to the new health gui…
  56. 56The speeds of an e-scooter (XX km/h) and a pedestrian (YY km/h) measured on a particular stretch of footpath are norma…
  57. 57A class of twenty four pupils consists of 11 girls and 13 boys. To form the class committee, four of the pupils are chos…
  58. 58In a school with a large number of students, p%p\%, where p>40p > 40, of its students study H2 Biology. In a random sample…
  59. 59In this question you should state the parameters of any distributions that you use. To regulate the use of its facil…
  60. 60The average number of railway accidents occurring along the North-South (NS) line in any one month is mm. Accidents occ…