Math topic中文

Tables venn tree techniques

Use of tables of outcomes, Venn diagrams, tree diagrams, and permutations and combinations techniques to calculate probabilities.

Practice questions

  1. 1Anthony plays a game using a four-sided fair die with the numbers 1, 2, 3 and 4 printed on its sides. Anthony rolls the…
  2. 2An amateur music composer is arranging a sequence of four musical notes followed by three beats. There are 7 possible no…
  3. 3The 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}…
  4. 4Two brothers Kai and Leo are duathlon (running and cycling) athletes who train regularly. For each day, the probability…
  5. 5A 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…
  6. 6A particular disease is known to infect approximately 1 in every 10 000 people. A test for this disease is 99.9% accurat…
  7. 7For 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…
  8. 8A group of 100 students are asked if they are student leaders, in a sports CCA, or studying in a science faculty. The nu…
  9. 9A 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…
  10. 10Kelly 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…
  11. 11Events 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,…
  12. 12Happie, the owner of a store selling novelty items, is organizing a publicity stunt for his store. Using a stock of ultr…
  13. 13A fruit seller sources his oranges from a supplier with a large plantation where 1% of the oranges are rotten. The suppl…
  14. 14Tetrahedral dice have four faces. Two fair tetrahedral dice, one red and one blue, have faces numbered 0, 1, 2, and 3 re…
  15. 15Section B: Statistics [60 marks] Given that events AA and BB are independent, show that A′A' and BB are also independ…
  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. 19The number of Green Top taxis and EZCab taxis arriving in a randomly chosen 10-minute period at the airport taxi bay may…
  20. 20For 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…
  21. 21In a supermarket lucky draw, a participant will first spin a wheel, followed by throwing a fair six-sided die. The wheel…
  22. 22Two fair n-sided dice, each with faces numbered 1, 2, ..., n, (where n≥4n \ge 4) are tossed in an experiment. The n…
  23. 23The table below shows the number of male and female students studying Chemistry, Physics and Biology at a private school…
  24. 24A 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…
  25. 25A bag contains 4 red counters and 6 blue counters. 4 counters are drawn from the bag at random, without replacement. Cal…
  26. 26A group of ten people consists of four single women, two single men and 2 couples. The ten people are arranged randomly…
  27. 27A group of seven people consisting of two single men, three single women and one married couple are arranged to be seate…
  28. 28In Sunny Island Republic, all male citizens are required to undergo a National Physical Fitness Assessment (NPFA) Test b…
  29. 29A 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…
  30. 30A group of 100 students are asked if they are student leaders, in a sports CCA, or studying in a science faculty. The nu…
  31. 31The Ang family, the Bao family and the Chew family have three, five and four members respectively. The three families ar…
  32. 32In 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…
  33. 33A particular disease is known to infect approximately 1 in every 10 000 people. A test for this disease is 99.9% accurat…
  34. 34在一个不透明的盒子中，放入22个红球，11个黄球和11个白球，这些球除颜色外都相同. (1)第一次摸出一个球后放回盒子中，搅匀后第二次再摸出一个球，请用列表法求出两次都摸到红球的概率;(2);(2)求一次同时摸出两个红球的…
  35. 35Two digits XX and YY are chosen independently at random from the set of 10 digits {0, 1, 2, . . . , 9}. Events AA and…
  36. 36The 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)…
  37. 37

    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…

  38. 38A tennis match is played between two players, AA and BB. The match consists of at most three sets. Each set is won by…
  39. 39The 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.…
  40. 40The bag contains 6 red discs, 6 green discs, 6 yellow discs and 6 blue discs. The discs are indistinguishable aside from…
  41. 41In a game, a player selects one ball at random from a bag which contains four balls numbered '1', '1', '2' and '3'. The…
  42. 42The National Aeronautics and Space Administration (NASA) compiles data on space shuttle launches and publishes them on i…
  43. 43In a school survey, a group of 80 students are asked about how much time per week (to nearest hour) they spend on their…
  44. 44Two fair 4-sided dice each has its faces labelled '1', '2', '3' and '4'. The two dice are thrown and the absolute differ…
  45. 45The bag contains 6 red discs, 6 green discs, 6 yellow discs and 6 blue discs. The discs are indistinguishable aside from…
  46. 46A bag contains 5 cards with the letter 'A', 3 cards with the letter 'B' and 2 cards with the letter 'C'. A A A A A B B B C C\text{A } \text{A } \text{A } \text{A } \text{A } \text{B } \text{B } \text{B } \text{C } \text{C}…
  47. 47The events A, B and C are such that P(A) = 0.8, P(B) = 0.2 and P(C) = 0.6. It is also known that P(A∩B)=P(B)P(A \cap B) = P(B) an…