Worksheet 6A (page 6.1)

1. P(choosing Terry)

2. (a) [Analysis: There are 16 integers, of which 8 integers are odd numbers.]

P(odd number)

(b) [Analysis: There are 16 integers, of which 4 integers are multiples of 5.]

P(multiple of 5)

3. (a) [Analysis: There are 6 letters in the word, of which 2 letters are ‘P’.]

P(‘P’)

(b) [Analysis: There are 6 letters in the word, of which 4 letters are not ‘E’.]

P(not ‘E’)

4. (a) [Analysis: There are 15 ballpoint pens in the box, of which 9 ballpoint pens are red or green.]

P(red ballpoint pen or green ballpoint pen)

(b) [Analysis: There are 15 ballpoint pens in the box, of which 10 ballpoint pens are not red.]

P(not a red ballpoint pen)

5. (a)

(b) 

\

Worksheet 6B (page 6.5)

1. (a) Experimental probability that the number is 1

(b) Experimental probability that the number is a multiple of 3

2. (a) Number of students

(b) (i) Probability that the student was not late for school in April

(ii) Probability that the number of late arrivals of the student in April is more than 2

3. (a) The relative frequency of the employees of the human resources department without any absence records last month

(b) The number of employees in the company without any absence records last month

Worksheet 6C (page 6.9)

1. / (a) / II
I / 1 / 2 / 3 / 4 / 5 / 6
1 / (1,1) / (1,2) / (1,3) / (1,4) / (1,5) / (1,6)
2 / (2,1) / (2,2) / (2,3) / (2,4) / (2,5) / (2,6)
3 / (3,1) / (3,2) / (3,3) / (3,4) / (3,5) / (3,6)
4 / (4,1) / (4,2) / (4,3) / (4,4) / (4,5) / (4,6)
5 / (5,1) / (5,2) / (5,3) / (5,4) / (5,5) / (5,6)
6 / (6,1) / (6,2) / (6,3) / (6,4) / (6,5) / (6,6)

(b) (i) Required probability

(ii) Required probability

2. / (a) / Second
ball
First
ball / / / / /

(b) Required probability

3. / (a) / II
I / / / / / / /

The total number of possible outcomes

(b) Required probability

4. (a) We can use a tree diagram to represent all the possible outcomes (i.e. sample space).

From the figure, the sample space is (H,H,H),

(H,H,T), (H,T,H), (H,T,T), (T,H,H),

(T,H,T), (T,T,H) and (T,T,T).

(b) Required probability

Worksheet 6D (page 6.13)

1. (a) Required probability

(b) Required probability

(c) Required probability

2. Total area

Area of the shaded region

\ P(hitting the shaded region)

3. Length of time between the arrivals of two trains at the station

Length of time for each train to stay in the station

\ Required probability

4. (a)

(b) Expected value of the number on the card drawn

Build-up Exercise 6A (page 6.17)

1. P(choosing Herbert)

2. P(aged under 16)

3. (a) P(‘M’)

(b) P(not ‘E’)

4. (a) P(black)

(b) P(face card)

5. According to the graph, 36 students have scored below 50.

\ P(passing the examination)

6. (a) P(red 10)

(b) P(diamond or ace)

(c) P(black or king)

7. (a) P(both piano and violin)

(b) P(only one kind of musical instrument)

8. According to the graph, there are 100 students in the group. 92 of them have scored below 80 and 72 have scored below 60.

\ P(getting a grade B)

9.  P(red dish or yellow dish)

\

10. Let x be the number of girls, then the number of boys is x+4.

\

\ P(girls)

11. Let x be the number of black balls, then the number of white balls is x+5.

 P(black ball)

\

\ The number of black balls is 3.

12. Let x be the number of red hats, then the number of white hats is x-4.

 P(red hats)

\

\ Total number of hats in the wardrobe

13. 

\

\ Total number of students

\ The number of students in S3A is 39.

14. Let y be the number of toy trains manufactured by machine B.

P(machine A)

\ The number of toy trains manufactured by

machine B is.

15. Let x be the number of additional tickets.

 P(radio)

\

\ 5 additional tickets with prizes of a radio

each should be provided.

16. Let x be the original number of raffle tickets, then the current number of the raffle tickets is x+240.

\ Number of tickets with prizes

=Original number of tickets

\ The original number of raffle tickets is 120.

17. (a) 

\

(b) 

\ Total number of cans of juice

(c) Number of cans of orange juice produced by the factory daily

18. (a) Let y be the number of bulbs produced by production line B.

P(production line A)

Total number of bulbs

P(production line B)

Total number of bulbs

\

\ The number of bulbs produced by

production line B is.

(b) P(production line A)

\ The number of bulbs produced by

production line A is 1000.

Build-up Exercise 6B (page 6.20)

19. Total number of the group of citizens

(a) Probability that the blood type of the citizen is O

(b) Probability that the blood type of the citizen is not AB

20. (a) Experimental probability of getting a packet with 42 marshmallows

(b) Experimental probability of getting a standard packet marshmallows

21. Total number of students

(a) Probability that the student’s I.Q. is between 95.5 and 105.5

(b) Probability that the student’s I.Q. is 105.5 or above

22. (a) Probability that the number of sleeping hours of Derek tonight is less than 8 hours

(b) Probability that the number of sleeping hours of Derek tonight is between 7 hours and 9 hours

23. (a) According to the graph, there are 40 students in S3C. 32 of them weigh less than 60kg and 6 weigh less than 40kg.

\ Probability that the weight of the student is between 40kg and 60kg

(b) According to the graph, there are 40 students in S3C. 22 of them weigh below 50kg.

\ Probability that the weight of the student is 50kg or above

24. Total number of members of the track and field team

(a) Probability that the member is a S1 boy

(b) Probability that the member is a girl

(c) Probability that the member is a S4 or S5 student

25. (a) (i) Experimental probability that the weight of a moon cake falls into the class interval 221g-230g

(ii) Experimental probability that the weight of a moon cake is between 210.5g and 240.5g

(iii) Experimental probability that the weight of a moon cake is 230.5g or above

(b) Number of moon cakes weighing 230.5g or above

26. (a) Relative frequency of the rotten eggs

(b) Number of rotten eggs

27. (a) Relative frequency of the misprinted copies

(b) Relative frequency of the copies without misprints

\ Number of copies without misprints

28. (a) (i) Experimental probability of drawing a black ballpoint pen

(ii) Experimental probability of drawing a ballpoint pen which is not green

(b) Number of black ballpoint pens

Experimental probability of drawing a red ballpoint pen

\ Number of red ballpoint pens

Experimental probability of drawing a green ballpoint pen

\ Number of green ballpoint pens

29. (a) Relative frequency of the fish in the pond with rings

(b) Relative frequency of the fish with rings

Number of fish with rings /
Number of fish in the pond
300 /
Number of fish in the pond

\ Number of fish in the pond

30. (a)

(b) (i) Experimental probability that the person watches the news channel most frequently

(ii) Experimental probability that the person watches the drama channel or entertainment channel most frequently

(c) News channel. It is because the news channel

is the paid channel which the people watch

most frequently in the evening.

(d) Number of people who watch the news channel most frequently

31. (a) Total frequency of drawing banknotes

(i) Experimental probability of drawing a $20 banknote

(ii) Experimental probability of drawing a $50 banknote

(iii) Experimental probability of drawing a $50 banknote

(b) See p.84 for the answer.

(c) Number of $20 banknotes

Build-up Exercise 6C (page 6.24)

32. / B
A / G / P / R
R / RG / RP / RR
W / WG / WP / WR
G / GG / GP / GR

(a) P(one red ball and one purple ball)

(b) P(two white balls)

(c) P(two balls of the same colour)

33. (a)

(b) The total number of possible outcomes is 8.

(c) P(2 sons and 1 daughter)

34. / II
I / 1 / 2 / 3 / 4 / 5 / 6
1 / (1,1) / (1,2) / (1,3) / (1,4) / (1,5) / (1,6)
2 / (2,1) / (2,2) / (2,3) / (2,4) / (2,5) / (2,6)
3 / (3,1) / (3,2) / (3,3) / (3,4) / (3,5) / (3,6)
4 / (4,1) / (4,2) / (4,3) / (4,4) / (4,5) / (4,6)
5 / (5,1) / (5,2) / (5,3) / (5,4) / (5,5) / (5,6)
6 / (6,1) / (6,2) / (6,3) / (6,4) / (6,5) / (6,6)

(a) P(only one of the numbers obtained is 2)

(b) P(at least one of the numbers obtained is a multiple of 3)

35. / II
I / 1 / 2 / 3 / 4 / 5 / 6
1 / (1,1) / (1,2) / (1,3) / (1,4) / (1,5) / (1,6)
2 / (2,1) / (2,2) / (2,3) / (2,4) / (2,5) / (2,6)
3 / (3,1) / (3,2) / (3,3) / (3,4) / (3,5) / (3,6)
4 / (4,1) / (4,2) / (4,3) / (4,4) / (4,5) / (4,6)
5 / (5,1) / (5,2) / (5,3) / (5,4) / (5,5) / (5,6)
6 / (6,1) / (6,2) / (6,3) / (6,4) / (6,5) / (6,6)

\ Event A is more likely to happen.

36. / (a) / D / I / S / A / B / L / E
A / AD / AI / AS / AA / AB / AL / AE
B / BD / BI / BS / BA / BB / BL / BE
I / ID / II / IS / IA / IB / IL / IE
L / LD / LI / LS / LA / LB / LL / LE
I / ID / II / IS / IA / IB / IL / IE
T / TD / TI / TS / TA / TB / TL / TE
Y / YD / YI / YS / YA / YB / YL / YE

(b) (i) P(two letters are the same)

(ii) P(two letters are consonants)

(iii) P(at least one of the letters is ‘I’)

37. / II
I / 1 / 2 / 3 / 4 / 5 / 6
1 / (1,1) / (1,2) / (1,3) / (1,4) / (1,5) / (1,6)
2 / (2,1) / (2,2) / (2,3) / (2,4) / (2,5) / (2,6)
3 / (3,1) / (3,2) / (3,3) / (3,4) / (3,5) / (3,6)
4 / (4,1) / (4,2) / (4,3) / (4,4) / (4,5) / (4,6)
5 / (5,1) / (5,2) / (5,3) / (5,4) / (5,5) / (5,6)
6 / (6,1) / (6,2) / (6,3) / (6,4) / (6,5) / (6,6)

(a) Required probability

(b) Required probability

38. / Kenneth
Macy / C / D / E
C / CC / CD / CE
D / DC / DD / DE
E / EC / ED / EE

(a) P(both of them select Highway C)

(b) P(they select the same route)

(c) P(none of them select Tunnel D)

39. / (a) / II
I / / / / / / /

(b) (i) P(two black balls)

(ii) P(two white balls)

(iii) P(two balls of the same colour)

(iv) P(one black ball and one white ball)

40. / Second scarf
First scarf / / / / /

(a) P(same scarf)

(b) P(scarves of the same colour)

41. See p.84 for the table.

(a) P(face values of two banknotes are the same)

(b) P(total amount is $100)

(c) P(total amount is more than $90)

42. (a)

From the figure above, the 3-digit numbers

that satisfy the condition are 222, 223, 232,

233, 322, 323, 332 and 333.

(b) (i) P(only one of the digits is ‘2’)

(ii) P(even number)

43. Let x be the number of yellow balls in the bag, then there are 2x purple balls in the bag.

\ There are 2 yellow balls and 4 purple balls in the bag.

Represent the 2 yellow balls by,, and the 4 purple balls by,,,.

II
I / / / / / /

(a) P(two purple balls)

(b) P(two balls in different colours)

44. Represent the red ball and white ball by R and W respectively.

II
I / R / W / W / Additional ball
R / W
R / RW / RW / RR / RW
W / WR / WW / WR / WW
W / WR / WW / WR / WW

(a) P(two balls in different colours)