1. Chapter 15 More about Probability Additional Example 15.1Additional Example 15.1 Additional Example 15.2Additional Example 15.2 Additional Example 15.3Additional Example 15.3 Additional Example 15.4Additional Example 15.4 Additional Example 15.5Additional Example 15.5 Additional Example 15.6Additional Example 15.6 Additional Example 15.7Additional Example 15.7 Additional Example 15.8Additional Example 15.8 Additional Example 15.9Additional Example 15.9 Additional Example 15.10Additional Example 15.10 Example 1Example 1 Example 2Example 2 Example 3Example 3 Example 4Example 4 Example 5Example 5 Example 6Example 6 Example 7Example 7 Example 8Example 8 Example 9Example 9 Example 10Example 10 New Trend Mathematics – S5A Quit

2. Chapter 15 More about Probability Additional Example 15.11Additional Example 15.11 Additional Example 15.12Additional Example 15.12 Additional Example 15.13Additional Example 15.13 Additional Example 15.14Additional Example 15.14 Example 11Example 11 Example 12Example 12 Example 13Example 13 Example 14Example 14 New Trend Mathematics – S5A Quit

3. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

4. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

5. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.1 There are 7 white balls, 4 black balls and 11 yellow balls in a bag. If a ball is drawn from the bag at random, what is the probability that the colour of the ball is (a)black? (b)black or white? (c)not white? (a)[ There are 22 balls in the bag. 4 of them are black balls. ] P(black) Solution: (b)[ There are 22 balls in the bag. 11 of them are black or white balls. ] P(black or white) (c)[ There are 22 balls in the bag. 15 of them are not white balls. ] P(not white)

6. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

7. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.2 The number of family members of S5A students is as follows: If a student is selected at random, find the probability that the number of family members of the student (a)is under 4. (b)is between 4 and 6 inclusive. (c)is either under 4 or over 6.

8. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.2 Solution: Total number of students in S5A  14  15  8  6  2  45 (a)[ The number of students who have less than 4 family members  14 ] P(under 4) (b)[ The number of students who have the number of family members between 4 and 6 inclusive  15  8  6  29 ] P(between 4 and 6 inclusive) (c)[The number of students who have less than 4 or more than 6 family members  14  2  16 ] P(under 4 or over 6)

9. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

10. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

11. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.3 The following table shows the monthly salaries of 100 fresh graduates. If one of these graduates is chosen at random, find the probability that the monthly salary of this graduate is above $10 000. Solution: ’ ‘ ’ ‘

12. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

13. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

14. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.4 In a lucky draw, the probabilities that the number drawn is smaller than 10, greater than 50 and between 15 and 30 are,, respectively. What is the probability of drawing a number (a)smaller than 10 or greater than 50? (b)between 15 and 30, or greater than 50? Solution: ’’ (a)

15. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.4 Solution: ’ ’(b)

16. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

17. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

18. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

19. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.5 Two computers are each used to generate a number. Computer A can generate numbers 1, 2, 3, 4 and 5 at random while computer B can generate numbers 1, 2, 3, 4, 5, 6 and 7 at random. Find the probability of getting (a)a sum of 6. (b)a product of 6. (c)two odd numbers. (d)a sum of 6 or a product of 6. (e)a sum of 6 or two odd numbers.

20. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.5 Solution: (a)Let X be the event of getting a sum of 6. Favourable outcomes are (1, 5), (2, 4), (3, 3), (4, 2) and (5, 1). 7654321  1   5 4 3 2   A B

21. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.5 Solution: (b)Let Y be the event of getting a product of 6. Favourable outcomes are (1, 6), (2, 3) and (3, 2). 7654321  1  5 4 3 2  A B

22. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.5 (d) Solution: (c)Let Z be the event of getting two odd numbers. Favourable outcomes are (1, 1), (1, 3), (1, 5), (1, 7), (3, 1), (3, 3), (3, 5), (3, 7), (5, 1), (5, 3), (5, 5) and (5, 7). 7654321 1 5 4 3 2 A B

23. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.5 Solution: (e) 7654321  1   5 4 3 2   A B

24. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

25. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.6 There are white, green and yellow balls in a bag. If a ball is drawn at random, the probability of getting a white ball is while that of getting a green ball is. (a)Find the probability of getting a ball which is not white in colour. (b)Find the probability of getting a yellow ball. Solution: LetW be the event of getting a white ball; G be the event of getting a green ball; Y be the event of getting a yellow ball.

26. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.6 Solution:

27. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

28. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.7 (a)[ Favourable outcomes of the sum to be less than or equal to 4 are (1, 1, 1), (1, 1, 2), (1, 2, 1) and (2, 1, 1). ] Solution: Three fair dice are tossed. Find the probability that (a)the sum is greater than 4. (b)the product is not an odd number.

29. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.7 (b)[Favourable outcomes of the product to be an odd number are (1, 1, 1), (1, 1, 3), (1, 1, 5), (1, 3, 1), (1, 3, 3), (1, 3, 5), (1, 5, 1), (1, 5, 3), (1, 5, 5), (3, 1, 1), (3, 1, 3), (3, 1, 5), (3, 3, 1), (3, 3, 3), (3, 3, 5), (3, 5, 1), (3, 5, 3), (3, 5, 5), (5, 1, 1), (5, 1, 3), (5, 1, 5), (5, 3, 1), (5, 3, 3), (5, 3, 5), (5, 5, 1), (5, 5, 3) and (5, 5, 5). ] Solution:

30. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

31. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.8 Solution: Let A be the event of Annie passing the test and B be the event of Jackie passing the test. (a) The probabilities for Annie and Jackie to pass a test are and respectively. Find the probability that (a)both of them pass the test. (b)both of them do not pass the test. (c)only one of them passes the test.

32. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.8 (c) Solution: (b)

33. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

34. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

35. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.9 There are 1 white T-shirt (W), 5 green T-shirts (G) and 2 black T-shirts (B) in a drawer. Three T-shirts are drawn randomly one by one with replacement. Find the probability that (a)all are black. (b)the first one is green, the second one is white and the third one is black. (c)all are different in colour. Solution: (a)

36. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.9 (b) Solution: (c)

37. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

38. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

39. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

40. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.10 There are two boxes A and B. Box A contains 4 green balls and 2 white balls. Box B contains 5 green balls, 3 white balls and 1 red ball. A ball is drawn from each box at random. Find the probability that (a) both balls are green. (b)one ball is green and one ball is red. (c)one ball is green and one ball is white. (d)at least one ball is white. Solution: ’’ (a)

41. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit (c) ’ ’ ’ ’ ’ ’ Additional Example 15.10 Solution: ’ ’(b)

42. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.10 (d) Solution: ’ ’

43. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

44. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

45. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

46. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.11 There are some white balls and black balls in three boxes A, B and C. The number of balls in each box is shown below: Now all the balls are put into a big box and a ball is drawn at random from this box, find the probability that (a)(i)the ball is black. (ii)the ball comes from box A. (iii)the ball is a black ball from box A. (b)the ball is black given that it comes from box B. (c)the ball comes from box C given that it is black.

47. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.11 Solution: Let K denote the event that the ball is black, and X denote the event that the ball comes from box A. Total number of balls  10  15  6  20  5  4  60 (a)(i) (ii) (iii)

48. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.11 Solution: (b)Let Y denote the event that the ball comes from box B.

49. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.11 Solution: (c)Let Z denote the event that the ball comes from box C.

50. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

51. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

52. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

53. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

54. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.12 [ The probability of the second draw depends on the first draw. ] Solution: From a pack of 52 playing-cards (without jokers), two cards are drawn at random one by one without replacement. Find the probability of getting (a)two red cards. (b)one spade and one king (excluding spade king). (c)at least one red card.

55. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.12 (b)Let S denote a spade excluding the spade king, K denote a king excluding the spade king. Solution: ’ ’

56. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.12 Solution:

57. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

58. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

59. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.13 Solution: Let X be the event that the black ball is transferred from box A to box B, and Y be the event that the black ball is transferred from box B to box C. (a) There are 5 red balls and 1 black ball in box A, 4 red balls in box B and nothing in box C. A ball is randomly transferred from box A to box B, and then a ball is randomly transferred from box B to box C. Find the probability that (a)the black ball is in box A. (b)the black ball is in box B. (c)the black ball is in box C.

60. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.13 Solution: (b)

61. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.13 Solution: (c)

62. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

63. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example

64. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.14 Solution: Let A denote the event that the product of the two outcomes is an even number. Two fair dice are tossed. Given that the product of the two outcomes is an even number, find the probability that (a)at least one outcome is ‘4’. (b)one outcome is an odd number.

65. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.14 Solution: (a)Let B denote the event that at least one outcome is ‘4’.  There are totally 6  6  36 possible outcomes for tossing two fair dice. For A and B to occur simultaneously, there are 11 possible results, i.e. (1, 4), (2, 4), (3, 4), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 4) and (6, 4).  Probability required

66. Chapter 15 More about Probability 2005 Chung Tai Educational Press © Quit Additional Example 15.14 Solution: (b)Let C denote the event that one outcome is an odd number.  There are totally 6  6  36 possible outcomes for tossing two fair dice. For A and C to occur simultaneously, there are 18 possible results, i.e.(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3) and (6, 5).  Probability required