Math topic中文

Mutually exclusive independent events

Mutually exclusive events and independent events.

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. 2The 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}…
  3. 3Two brothers Kai and Leo are duathlon (running and cycling) athletes who train regularly. For each day, the probability…
  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. 6A group of 100 students are asked if they are student leaders, in a sports CCA, or studying in a science faculty. The nu…
  7. 7For 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…
  8. 8Events 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,…
  9. 9设AA，BB为相互独立事件，下列命题中正确的是()(\quad) A. AA与BB是对立事件 B. AA与BB是互斥事件 C. AA与B‾\overline{B}是相互独立事件 D. A‾\overline{A}…
  10. 10Section B: Statistics [60 marks] Given that events AA and BB are independent, show that A′A' and BB are also independ…
  11. 11Tim plays a game with 3 outcomes having the score of 2, 5 and 6. The corresponding probabilities are 27\dfrac{2}{7}, kk…
  12. 12A store owner receives a shipment of stationery items, including notebooks, pens, and correction tapes. Historical data…
  13. 13**In this question, you should state clearly all the distributions that you use, together with the values of the appropr…
  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. 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. 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 probability of obtaining a head when a particular coin is tossed is pp. A fair cubical die has the number '1' on on…
  21. 21在东京奥运会中，甲、乙、丙三名跳水运动员参加小组赛，已知甲晋级的概率为p(0<p<1)p(0< p< 1)，乙、丙晋级的概率均为q(0<q<1)q(0< q< 1)，且三人是否晋级相互对立. (1)若甲成功晋级的概率与乙、丙两人均没有晋级的概率相等，与乙、…
  22. 22The average number of calls per hour received by telephone operators at the Call Centre of bank ECBC is being reviewed.…
  23. 23Two 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…
  24. 24The number of Green Top taxis and EZCab taxis arriving in a randomly chosen 10-minute period at the airport taxi bay may…
  25. 25For 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…
  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. 27Two families plan to go on a hiking trip together. There are 10 people from the Lee family, consisting of 3 married coup…
  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. 30A class of twenty-five pupils consists of 15 girls and 10 boys. At the beginning of the year four pupils are to be chose…
  31. 31On a Friday evening, the class chairperson emails his 20 classmates to propose an outing to watch a newly released actio…
  32. 32Two fair n-sided dice, each with faces numbered 1, 2, ..., n, (where n≥4n \ge 4) are tossed in an experiment. The n…
  33. 33The table below shows the number of male and female students studying Chemistry, Physics and Biology at a private school…
  34. 34A credit card company has a special 24-hour telephone hotline for customers to either report a lost credit card or to re…
  35. 35At a particular game stall, players throw darts at a target board to earn points for redeeming prizes. The target board…
  36. 36Alice uses a computer program to simulate 80 tosses of a biased coin. Let YY be the random variable denoting the number…
  37. 37During the Great Mega Sale, the waiting times, in minutes, for men and women, at their respective fitting rooms, have me…
  38. 38A bag contains 4 red counters and 6 blue counters. 4 counters are drawn from the bag at random, without replacement. Cal…
  39. 39At the drinks stall in a canteen, both hot and cold drinks are sold. The number of hot drinks sold per minute follows a…
  40. 40State with a reason whether or not the events "at least 3 blue counters are drawn" and "at least 1 counter of each colou…
  41. 41设事件AA，BB相互独立，P(A)=0.6P\left(A\right)=0.6，P(B)=0.3P\left(B\right)=0.3，则P(AB‾∪A‾B)=()P(A\overline{B}∪\overline{A}B)=(\quad) A. 0.36                             0.36\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: …
  42. 42A factory manufactures a large number of chips in a variety of colours and packs them into boxes. Each box contains 36 r…
  43. 43A 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…
  44. 44The finishing times in a 10km race with a large number of runners follow a normal distribution. After 40 minutes, 10% of…
  45. 45A group of 100 students are asked if they are student leaders, in a sports CCA, or studying in a science faculty. The nu…
  46. 46In 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…
  47. 47A 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\}…
  48. 48An eatery is giving out free burgers in a promotion to celebrate its anniversary. A total of 80 burgers, consisting of 8…
  49. 49A particular disease is known to infect approximately 1 in every 10 000 people. A test for this disease is 99.9% accurat…
  50. 50Students seeking admission to Kingdom University and Island University are required to apply using their national examin…
  51. 51Each square in a 3×33 \times 3 grid is randomly filled with one of the 4 gray-and-white tiles shown below on the left. Wh…
  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. 54

    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…

  55. 55In this question you should state the parameters of any distributions that you use. To regulate the use of its facil…
  56. 56The average number of railway accidents occurring along the North-South (NS) line in any one month is mm. Accidents occ…
  57. 57The 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.…
  58. 58A company produces ceramic vases. A fixed number of randomly chosen vases are inspected each day and the number of defec…
  59. 59The National Aeronautics and Space Administration (NASA) compiles data on space shuttle launches and publishes them on i…
  60. 60A bag contains 10 red and 15 green beads which are indistinguishable apart from colour. Beads are drawn from the bag sin…