Math topic中文

Conditional probability

Calculation of conditional probabilities in simple cases.

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. 5Events 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,…
  6. 6For 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…
  7. 7The 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…
  8. 8A team of 15 students was selected for an outdoor education trip. One student volunteered to be the trip leader while an…
  9. 9For 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…
  10. 10A bakery produces batches of cookies. On average, the proportion of flawed cookies produced is pp, where 0<p<10 < p < 1. T…
  11. 11The average number of calls per hour received by telephone operators at the Call Centre of bank ECBC is being reviewed.…
  12. 12A nursery supplies plants to Evergreen Pte. Ltd. The heights, in centimetres, of plants supplied may be taken to follow…
  13. 13[For this question, you should state clearly the values of the parameters of any normal distribution you use.] After din…
  14. 14Two 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…
  15. 15The number of Green Top taxis and EZCab taxis arriving in a randomly chosen 10-minute period at the airport taxi bay may…
  16. 16A 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…
  17. 17Two families plan to go on a hiking trip together. There are 10 people from the Lee family, consisting of 3 married coup…
  18. 18In a supermarket lucky draw, a participant will first spin a wheel, followed by throwing a fair six-sided die. The wheel…
  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. 20A bag contains 10 red and 15 green beads which are indistinguishable apart from colour. Beads are drawn from the bag sin…
  21. 21A class of twenty-five pupils consists of 15 girls and 10 boys. At the beginning of the year four pupils are to be chose…
  22. 22The diagram below shows a circular target board of radius 40 cm, divided by two concentric circles of radii 12 cm and 24…
  23. 23To reduce the number of speeding incidents on the road, traffic police in Country S set up traffic cameras at 3 busy tra…
  24. 24Two fair n-sided dice, each with faces numbered 1, 2, ..., n, (where n≥4n \ge 4) are tossed in an experiment. The n…
  25. 25The table below shows the number of male and female students studying Chemistry, Physics and Biology at a private school…
  26. 26设P(A∣B)=P(B∣A)=12,P(A)=13P(A|B)=P(B|A)=\dfrac{1}{2},P(A)=\dfrac{1}{3}，则P(B)P(B)等于()(\quad) A. 12\dfrac{1}{2} B. 13\dfrac{1}{3} C. 14\dfrac{1}{4}…
  27. 27Alice uses a computer program to simulate 80 tosses of a biased coin. Let YY be the random variable denoting the number…
  28. 28A 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…
  29. 29A bag contains 4 red counters and 6 blue counters. 4 counters are drawn from the bag at random, without replacement. Cal…
  30. 30At the drinks stall in a canteen, both hot and cold drinks are sold. The number of hot drinks sold per minute follows a…
  31. 31A gathering of 12 people break into 3 groups of 4 to play 3 different games: carrom, UNO and bridge. Find the number of…
  32. 32A group of seven people consisting of two single men, three single women and one married couple are arranged to be seate…
  33. 33In Sunny Island Republic, all male citizens are required to undergo a National Physical Fitness Assessment (NPFA) Test b…
  34. 34A factory manufactures a large number of chips in a variety of colours and packs them into boxes. Each box contains 36 r…
  35. 35A 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…
  36. 36The finishing times in a 10km race with a large number of runners follow a normal distribution. After 40 minutes, 10% of…
  37. 37A manufacturing company produces surgical masks. The surgical masks are randomly packed into boxes of 50. On average, 15…
  38. 38Serene plays a simple online game which moves a counter one step at a time along a straight line. The counter starts fro…
  39. 39An eatery is giving out free burgers in a promotion to celebrate its anniversary. A total of 80 burgers, consisting of 8…
  40. 40A particular disease is known to infect approximately 1 in every 10 000 people. A test for this disease is 99.9% accurat…
  41. 41Two digits XX and YY are chosen independently at random from the set of 10 digits {0, 1, 2, . . . , 9}. Events AA and…
  42. 42The 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)…
  43. 43In each batch of pralines that a chocolate factory produces, they are packed into boxes of 16. Due to the new health gui…
  44. 44

    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…

  45. 45For 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…
  46. 46The average number of railway accidents occurring along the North-South (NS) line in any one month is mm. Accidents occ…
  47. 47A tennis match is played between two players, AA and BB. The match consists of at most three sets. Each set is won by…
  48. 48Ai Ming plays a computer game with Shu Ting, where they each shoot at a target. For each shot, the probability that the…
  49. 49A company produces ceramic vases. A fixed number of randomly chosen vases are inspected each day and the number of defec…
  50. 50一个袋中装有大小相同的22个白球和33个黑球，若不放回地依次任取两个球，设事件AA为“第一次取出白球”，事件BB为“第二次取出黑球”，则在AA发生的条件下BB发生的概率为()(\quad) A. 13\dfrac{1}{3}…
  51. 51A bag contains 10 red and 15 green beads which are indistinguishable apart from colour. Beads are drawn from the bag sin…
  52. 52A manufacturer produces screen protectors for handphones. On average, 4% of the screen protectors are cracked. The scree…
  53. 53In a school survey, a group of 80 students are asked about how much time per week (to nearest hour) they spend on their…
  54. 54Three red balls and two blue balls are placed in a bag. All the balls are indistinguishable except for their colours. Mr…
  55. 55一个袋中有3个红球和5个白球，不放回地连取2个球，求两个都是红球的概率。
  56. 56In each batch of pralines that a chocolate factory produces, they are packed into boxes of 16. Due to the new health gui…
  57. 57A 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}…
  58. 58The 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…
  59. 59A roller-coaster ride has two separate safety systems to detect faults on the track and on the roller-coaster train itse…