Math topic中文

Standard results

Use of:

  • P(A′)=1−P(A)\mathrm{P}(A')=1-\mathrm{P}(A)
  • P(A∪B)=P(A)+P(B)−P(A∩B)\mathrm{P}(A\cup B)=\mathrm{P}(A)+\mathrm{P}(B)-\mathrm{P}(A\cap B)
  • P(A∩B)=P(A∣B) P(B)\mathrm{P}(A\cap B)=\mathrm{P}(A\mid B)\,\mathrm{P}(B)

Practice questions

  1. 1The events AA and BB are such that P(B)=13\mathrm{P}(B) = \frac{1}{3}, P(A∣B)=25\mathrm{P}(A|B) = \frac{2}{5} and P(A∪B)=35\mathrm{P}(A \cup B) = \frac{3}{5}…
  2. 2Two brothers Kai and Leo are duathlon (running and cycling) athletes who train regularly. For each day, the probability…
  3. 3A 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…
  4. 4A particular disease is known to infect approximately 1 in every 10 000 people. A test for this disease is 99.9% accurat…
  5. 5For events AA and BB it is given that P(A)=0.55\mathrm{P}(A) = 0.55, P(B)=0.65\mathrm{P}(B) = 0.65 and P(A∪B)=0.93\mathrm{P}(A \cup B) = 0.93…
  6. 6For events AA and BB, it is given that P(A′)=0.3\mathrm{P}(A') = 0.3 and P(B)=0.55\mathrm{P}(B) = 0.55. Given that the events AA an…
  7. 7Events AA and BB are such that P(A)=0.7P(A)=0.7 and P(B)=0.8P(B)=0.8. Show that P(A∩B)≥0.5P(A \cap B) \ge 0.5 If P(A′ ∪ B)=0.85P(A'\ \cup\ B)=0.85,…
  8. 8A fruit seller sources his oranges from a supplier with a large plantation where 1% of the oranges are rotten. The suppl…
  9. 9A credit card company has a special 24-hour telephone hotline for customers to either report a lost credit card or to re…
  10. 10The letters from the word PERIMETER are arranged in a row. Find the number of different arrangements of the nine letters…
  11. 11A circular target board is made up of 3 concentric circles as shown below. The circles have the same centre and their ra…
  12. 12Section B: Statistics [60 marks] Given that events AA and BB are independent, show that A′A' and BB are also independ…
  13. 13A store owner receives a shipment of stationery items, including notebooks, pens, and correction tapes. Historical data…
  14. 14In this question you should clearly state the values of the appropriate parameters of any distributions used. The diamet…
  15. 15For 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…
  16. 16The events AA, BB and CC are such that P(A)=0.1\mathrm{P}(A) = 0.1, P(B)=0.2\mathrm{P}(B) = 0.2 and P(C)=c\mathrm{P}(C) = c. AA and…
  17. 17Section B: Probability and Statistics [60 marks] If P(B∣A)=0.2\text{P}(B \mid A) = 0.2, P(A∣B)=0.6\text{P}(A \mid B) = 0.6 and P(A′∩B′)=0.3\text{P}(A' \cap B') = 0.3…
  18. 18A team of 15 students was selected for an outdoor education trip. One student volunteered to be the trip leader while an…
  19. 19For events A and B, it is given that P(A∪B′)=23P(A \cup B') = \frac{2}{3} and P(A)=14P(A) = \frac{1}{4}. Find P(A∣A∪B)P(A \mid A \cup B). G…
  20. 20The random variable XX is normally distributed with mean μ\mu and variance σ2\sigma^2. Find P(X>μ+0.05σ)\mathrm{P}(X > \mu + 0.05\sigma)…
  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. 22Two events AA and BB are such that P(A)=pP(A)=p and P(B)=54pP(B)=\frac{5}{4}p. It is given that P(A∪B)=P(A∣B)=0.6P(A\cup B)=P(A\mid B)=0.6. Fin…
  23. 23The number of Green Top taxis and EZCab taxis arriving in a randomly chosen 10-minute period at the airport taxi bay may…
  24. 24For the events AA, BB and CC it is given that P(A)=P(A∩B)=15P(A) = P(A \cap B) = \tfrac{1}{5} and P(B)=2P(A)P(B) = 2P(A). It is also give…
  25. 25In this question you should state clearly the parameters of any normal distributions you use. The masses in kilograms of…
  26. 26A 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…
  27. 27The random variable XX has distribution N(μ,σ2)\mathrm{N}(\mu, \sigma^2). Given that P(X>k)=0.45\mathrm{P}(X > k) = 0.45, find the va…
  28. 28The number of Green Top taxis and EZCab taxis arriving in a randomly chosen 10-minute period at the airport taxi bay may…
  29. 29A bag contains 10 red and 15 green beads which are indistinguishable apart from colour. Beads are drawn from the bag sin…
  30. 30To reduce the number of speeding incidents on the road, traffic police in Country S set up traffic cameras at 3 busy tra…
  31. 31The table below shows the number of male and female students studying Chemistry, Physics and Biology at a private school…
  32. 32Green Earth Factory produces solar panels. On average, 2% of the solar panels produced are found to contain defects. The…
  33. 33A 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…
  34. 34A bag contains 4 red counters and 6 blue counters. 4 counters are drawn from the bag at random, without replacement. Cal…
  35. 35At the drinks stall in a canteen, both hot and cold drinks are sold. The number of hot drinks sold per minute follows a…
  36. 36A group of ten people consists of four single women, two single men and 2 couples. The ten people are arranged randomly…
  37. 37In Sunny Island Republic, all male citizens are required to undergo a National Physical Fitness Assessment (NPFA) Test b…
  38. 38A 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…
  39. 39A 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"…
  40. 40The finishing times in a 10km race with a large number of runners follow a normal distribution. After 40 minutes, 10% of…
  41. 41A manufacturing company produces surgical masks. The surgical masks are randomly packed into boxes of 50. On average, 15…
  42. 42某市气象局预报称：明天本市的降水概率为80%，这句话指的是（ ） A. 明天本市80%的时间下雨，20%的时间不下雨 B. 明天本市一定下雨 C. 明天本市80%的地区下雨，20%的地区不下雨 D. 明天本市不下雨的可能性只有20%
  43. 43The Ang family, the Bao family and the Chew family have three, five and four members respectively. The three families ar…
  44. 44To maintain the good condition of library books, any book with more than 7 defects will be donated away. The mean number…
  45. 45A shop sells apples in bags of 12. The average number of unripe apples in a bag is 2.16. State two assumptions needed fo…
  46. 46Cars arrive at a jetty randomly at an average rate of one every 5 minutes. From the jetty, a ferry transports the cars t…
  47. 47Epple Company manufactures a large number of E-phones. It is known that 1% of the E-phones manufactured are defective. A…
  48. 48A 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\}…
  49. 49一袋中有55个白球，33个红球，现从袋中往外取球，每次任取一个记下颜色后放回，直到红球出现1010次时停止，设停止时共取了ξξ次球，则P(ξ=12)P(ξ=12)等于()() A. C1210(38)10⋅(58)2C_{12}^{10}( \dfrac {3}{8})^{10}⋅( \dfrac {5}{8})^{2}…
  50. 50**In this question you should state clearly all the distributions that you use, together with the values of the appropri…
  51. 51An eatery is giving out free burgers in a promotion to celebrate its anniversary. A total of 80 burgers, consisting of 8…
  52. 52Two digits XX and YY are chosen independently at random from the set of 10 digits {0, 1, 2, . . . , 9}. Events AA and…
  53. 53The events AA, BB and CC are such that P(A)=0.8P(A)=0.8, P(B)=0.2P(B)=0.2 and P(C)=0.6P(C)=0.6. It is also known that P(A∩B)=P(B)P(A\cap B)=P(B)…
  54. 54A class of twenty four pupils consists of 11 girls and 13 boys. To form the class committee, four of the pupils are chos…
  55. 55

    Section B: Probability and Statistics [60 marks] For events AA and BB, it is given that P(B′)=0.51\mathrm{P}(B') = 0.51 an…

  56. 56For events AA, BB and CC, it is given that P(A)=0.7P(A)=0.7, P(B)=0.5P(B)=0.5, P(C∣A′)=0.6P(C\mid A')=0.6 and P(A∣C′)=0.76P(A\mid C')=0.76. Find the…
  57. 57The average number of railway accidents occurring along the North-South (NS) line in any one month is mm. Accidents occ…
  58. 58The events AA and BB are such that P(A)=a\text{P}(A) = a and P(B)=b\text{P}(B) = b. AA and BB are mutually exclusive events.…
  59. 59A company produces ceramic vases. A fixed number of randomly chosen vases are inspected each day and the number of defec…
  60. 60It is known that 8% of the population of a large city use a particular web browser called Voyager. A researcher wishes t…