Mathematics Form 4

1

ACTIVITY SHEET

Pupils copy

LESSON 80: Possible Outcome of an Experiment.

1 Khatijah throws a dice. Determine whether the following are possible outcomes.

(a) 5 (b) 3 (c) 8 (d) an even number (e) a multiple of 7

2 Noor and Vijaya are playing Chongkak which has seven holes in each row. Siti is

watching the game. Determine if the following outcomes are possible. (a) Noor finally has 8 empty (burnt) holes. (b) Vijaya wins the game. (c) Siti loses the game. (d) After one round of the game, both Noor and Vijaya have the same number of

empty or burnt holes. 3 There are two bags. The first bag contains five cards with different numbers. The

numbers are 4, 6, 9, 12 and 15. The second bag contains three cards with different letters, which are A, C and E. If one card is taken randomly from each bag, determine whether the following (in the form of ordered pairs) are possible outcomes. (a) (4, E) (b) (4, 15) (c) (a prime number, C) (d) (an even number, A) (e) (9, D)

4 A spinner with the numbers which are all the factors of 36 is spun. List all the

possible outcomes. 5 A coin is tossed three times. Draw a tree diagram to list all the possible outcomes

of this experiment.

Mathematics Form 4

2

ACTIVITY SHEET

Teachers copy

LESSON 80: Possible Outcome of an Experiment.

1 Khatijah throws a dice. Determine whether the following are possible outcomes.

(a) 5 Possible (b) 3 Possible (c) 8 Impossible (d) an even number Possible (e) a multiple of 7 Impossible

2 Noor and Vijaya are playing Chongkak which has seven holes in each row. Siti is

watching the game. Determine if the following outcomes are possible. (a) Noor finally has 8 empty (burnt) holes. Impossible (b) Vijaya wins the game. Possible (c) Siti loses the game. Impossible (d) After one round of the game, both Noor and Vijaya have the same number of

empty or burnt holes. Impossible 3 There are two bags. The first bag contains five cards with different numbers. The

numbers are 4, 6, 9, 12 and 15. The second bag contains three cards with different letters, which are A, C and E. If one card is taken randomly from each bag, determine whether the following (in the form of ordered pairs) are possible outcomes. (a) (4, E) Possible (b) (4, 15) Impossible (c) (a prime number, C) Impossible (d) (an even number, A) Possible (e) (9, D) Impossible

4 A spinner with the numbers which are all the factors of 24 is spun. List all the

possible outcomes. The possible outcomes are 1, 2, 3, 4, 6, 8, 12, and 24. 5 A coin is tossed three times. Draw a tree diagram to list all the possible outcomes

of this experiment.

H

T

H

T

H

TH

TH

TH

T

H

T

(H, H, H)

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

(H, T, T)

(T, H, H)

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

(T, T, T)

Mathematics Form 4

1

ACTIVITY SHEET

Pupils Copy

LESSON 81: Sample Space of an Experiment.

For each of the following,

i ) List all the possible outcomes ii ) Write the sample space by using set notations. 1. The experiment of tossing two fair coins simultaneously.

(i) ...

(ii)

2. The experiment of tossing a fair coin twice.

(i) ...

(ii)

3. The experiment of picking an alphabet from the word COURSEWARE.

(i) ...

(ii)

4. A spinner with the numbers 7, 8, 9 is spun twice.

(i) ...

(ii)

5. A ball is selected at random from a bag containing 3 red balls, 2 blue balls and 4 green balls.

(i) ...

(ii)

6. An experiment of rolling a fair dice.

(i) ...

(ii)

7. Randomly select a marble from a box containing one blue marble and three yellow marbles.

(i) ...

(ii)

8. Randomly select a digit from the number 4894.

(i) ...

(ii)

Mathematics Form 4

2

ACTIVITY SHEET

Teachers Copy

LESSON 81: Sample Space of an Experiment.

For each of the following, i ) List all the possible outcomes ii ) Write the sample space by using set notations. 1. The experiment of tossing two fair coins simultaneously.

(i) HH, HT, TH, TT or (H, H), (H, T), (T, H), (T, T) (ii) S = {HH, HT, TH, TT} or S = {(H, H), (H, T), (T, H), (T, T)}

2. The experiment of tossing a fair coin twice.

(i) HH, HT, TH, TT or (H, H), (H, T), (T, H), (T, T) (ii) S = {HH, HT, TH, TT} or S = {(H, H), (H, T), (T, H), (T, T)}

3. The experiment of picking an alphabet from the word COURSEWARE.

(i) C, O, U, R, S, E, W, A, R, E (ii) S = {C, O, U, R, S, E, W, A, R, E}

4. A spinner with the numbers 7, 8, 9 is spun twice.

(i) (7,7), (7,8), (7,9), (8,7), (8,8), (8,9), (9,7), (9,8), (9,9) (ii) S = {(7,7), (7,8), (7,9), (8,7), (8,8), (8,9), (9,7), (9,8), (9,9)}

5. A ball is selected at random from a bag containing 3 red balls, 2 blue balls and 4

green balls.

(i) R1, R 2, R3, B1, B2, G1, G2, G3, G4 (ii) S = { R1, R2, R3, B1, B2, G1, G2, G3, G4 }

where R = red, B = blue, G = green

6. An experiment of rolling a fair dice.

(i) 1, 2, 3, 4, 5, 6 (ii) S = {1, 2, 3, 4, 5, 6}

7. Randomly select a marble from a box containing one blue marble and three

yellow marbles.

(i) B1, Y 1, Y2, Y 3 (ii) S = {B1, Y 1, Y2, Y3}

where Y = yellow, B = blue

8. Randomly select a digit from the number 4894.

(i) 4,8,9,6 (ii) S = {4, 8, 9, 6}

Mathematics Form 4

1

ACTIVITY SHEET

Pupils Copy

LESSON 82: Elements of a Sample.

An aquarium contains two gold fishes and a flower-horn fish. If Dina randomly catches 2 fishes consequently from the aquarium, identify the elements of the sample space and the following events (Let G = gold fish, F = flower-horn fish)

Answer: a. Sample space using set notations

Answer: b. One gold fish and one flower-horn fish are caught.

Answer:

c. Two gold fishes are caught.

A drawer has five number card; each labeled 3, 4, 5, 6 or 7. Two cards are picked randomly from the drawer. State the elements that satisfy the following conditions.

Answer: a. The sum of the two numbers is equal to 10.

Answer:

b. The product of the two numbers is greater than 14.

Answer:

c. Getting odd numbers.

Two balls are drawn simultaneously from a bag containing a blue ball, a green ball and a yellow ball.

Answer: a. Write the sample space of this experiment using set notations.

Answer:

b. List the elements of getting a yellow ball.

Answer:

c. List the elements of getting a blue ball and a yellow ball.

A dice is rolled, list the following events.

Answer: a. P = the event of getting an even number.

Answer:

b. Q = the event of getting a prime number.

Five number cards; 3, 4, 5, 6, 7

Mathematics Form 4

2

ACTIVITY SHEET

Teachers Copy

LESSON 82: Elements of a Sample.

An aquarium contains two gold fishes and a flower-horn fish. If Dina randomly catches 2 fishes consequently from the aquarium, identify the elements of the sample space and the following events ( Let G = gold fish, F = flower-horn fish)

Answer: a. Sample space using set notations

S = { G1G2, G1F,G2G1, G2F, FG1, FG2 }

Answer: b. One gold fish and one flower-horn fish are caught.

B = { G1F,G2F, FG1, FG2 }

Answer:

c. Two gold fishes are caught. C = { G1G2, G2G1 }

A drawer has five number card; each labeled 3, 4, 5, 6 or 7. Two cards are picked randomly from the drawer. State the elements that satisfy the following conditions.

Answer: a. The sum of the two numbers is equal to 10.

Q = { (3,7) (4,6) } Answer:

b. The product of the two numbers is greater than 14. F = {(3,5), (3,6), (3,7), (4,5), (4,6), (4,7), (5,6), (5,7), (6,7)} Answer:

c. Getting odd numbers. H = {(3,5), (3,7), (5, 3), (5,7), (7,3), (7,5)}

Two balls are drawn simultaneously from a bag containing a blue ball, a green ball and a yellow ball.

Answer: a. Write the sample space of this experiment using set notations. S = {BG, BY, GB, GY,

YB, YG} Answer:

b. List the elements of getting a yellow ball. Q = {BY, GY, YB, YG}

Answer:

c. List the elements of getting a blue ball and a yellow ball. T = {BY, YB}

A dice is rolled, list the following events.

Answer: a. P = the event of getting an even number.

P = {2, 4, 6}

Answer:

b. Q = the event of getting a prime number. T = {2, 3, 5}

Five number cards; 3, 4, 5, 6, 7

Mathematics Form 4

1

ACTIVITY SHEET

Pupils Copy

LESSON 83: Probability.

An aquarium contains two gold fishes, three flower-horn fishes and four carp fishes. If Siti randomly catches 2 fishes consequently from the aquarium, determine whether the following events are possible or impossible:

Answer: a. One gold fish and one flower-horn fish are caught.

Answer: b. One carp fish and one talapia fish are caught.

Answer:

c. Two gold fishes are caught.

A glove factory produces 1200 pairs of gloves, and 300 pairs are defected. Each pair of gloves are tied together with a string. A pair of gloves is picked randomly.

Answer: a. Find the ratio that the gloves are not defected.

Answer:

b. Find the ratio that the gloves are defected.

A drawer contains a pair of blue socks, two pairs of purple socks and a pair of red socks. If a sock is randomly selected from the drawer, what is the probability that:

Answer: a. the sock is purple

Answer:

b. the sock is blue or red Answer:

c. the sock is red or purple

In a National Day celebration, 10 000 peoples participate in the national march. 4000 of them wear soldier uniforms, 2500 wear police uniforms, 500 wear fireman uniforms and the rest are a variety of other uniforms. If the best uniform wi ll be rewarded among the participants, what is probability that:

Answer: a. a soldier will win the reward?

Answer:

b. a policeman will win the reward?

Answer:

c. a fireman will win the reward?

A dice is rolled. Determine the probability for the following outcomes:

Answer: a. An odd number that is greater than 3 is obtained.

Answer: b. A prime number is obtained.

Answer:

c. A number less than 4 is obtained.

A pair of blue socks, two pairs of purple socks,a pair of red socks.

Mathematics Form 4

2

ACTIVITY SHEET

Teachers Copy

LESSON 83: Probability.

An aquarium contains two gold fishes, three flower-horn fishes and four carp fishes. If Siti randomly catches 2 fishes consequently from the aquarium, determine whether the following events are possible or impossible:

Answer: a. One gold fish and one flower-horn fish are caught.

Possible

Answer: b. One carp fish and one talapia fish are caught.

Impossible

Answer:

c. Two gold fishes are caught. Possible

A glove factory produces 1200 pairs of gloves, and 300 pairs are defected. Each pair of gloves are tied together with a string. A pair of gloves is picked randomly.

Answer: a. Find the ratio that the gloves are not defected.

900/1200 = 3/4

Answer:

b. Find the ratio that the gloves are defected. 300/1200 = 1/4

A drawer contains a pair of blue sock, two pairs of purple socks and a pair of red sock. If a sock is randomly selected from the drawer, what is the probability that:

Answer: a. the sock is purple.

4/8 = 1/2 Answer:

b. the sock is blue or red. 4/8 = 1/2 Answer:

c. the sock is red or purple. 6/8 = 3/4

In a National Day celebration, 10 000 peoples participate in the national march. 4000 of them wear soldier uniforms, 2500 wear police uniforms, 500 wear fireman uniforms and the rest are a variety of other uniforms. If the best uniform will be rewarded among the participants, what is probability that:

Answer: a. a soldier will win the reward?

4000/10000 = 2/5 Answer:

b. a policeman will win the reward? 2500/10000 = 1/4

Answer:

c. a fireman will win the reward? 500/10000 = 1/20

A dice is rolled. Determine the probability for the following outcomes:

Answer: a. An odd number that is greater than 3 is obtained.

1/6

Answer: b. A prime number is obtained.

4/6 = 2/3

Answer:

c. A number less than 4 is obtained. 3/6 = 1/2

A pair of blue socks, two pairs of purple socks,a pair of red socks.

Mathematics Form 4

1

ACTIVITY SHEET Pupils Copy LESSON 84: Problems on probability

Answer all the questions. 1 The probability of getting a red card from one box is 0.45. If there are 100

coloured cards in the box, how many can you expect to be red cards?

2 A group of students were selected from a class to attend a meeting. If the

probability of choosing a student who is wearing a pair of spectacles is 41

estimate the number of students wearing spectacles from a group of 120 students.

3 In a class, the probability of choosing a girl is 53 . If there are 15 girls in the class,

(a) Calculate the number of students in the class.

(b) If the number of students is increased, estimate the number of girls in a group of 200 students.

Mathematics Form 4

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4 In a survey on 200 consumers in an area, the following information was obtained.

Type of detergent Brand A Brand B Brand C Brand D Brand E

Frequency 40 55 10 50 45

(a) If a consumer is selected at random, find the probability that the consumer

(i) uses Brand B

(ii) uses Brand A or Brand D

(b) If 1500 consumers were selected from that area, how many would you predict to use Brand C?

Mathematics Form 4

3

ACTIVITY SHEET Teachers Copy LESSON 84: Problems on probability

Answer all the questions. 1 The probability of getting a red card from one box is 0.45. If there are 100

coloured cards in the box, how many can you expect to be red cards?

Expected number of red cards = Probability of getting a red card number of cards

= 0.45 100 = 45

2 A group of students were selected from a class to attend a meeting. If the

probability of choosing a student who is wearing a pair of spectacles is 41

estimate the number of students wearing spectacles from a group of 120 students.

Expected number of students = Probability of choosing a student who is who are wearing spectacles wearing spectacles 120 students

= 41

120

= 30

3 In a class, the probability of choosing a girl is 53 . If there are 15 girls in the class,

(a) Calculate the number of students in the class. Let x = number of students. Using ratio,

53

= x

15

35

=x 15

=x 25 Therefore, the number of students in the class is 25.

(b) If the number of students is increased, estimate the number of girls in a group of 200 students.

Expected number of girls = the probability of choosing a girl 200

= 53

200

= 120

Mathematics Form 4

4

4 In a survey on 200 consumers in an area, the following information was obtained.

Type of detergent Brand A Brand B Brand C Brand D Brand E

Frequency 40 55 10 50 45

(a) If a consumer is selected at random, find the probability that the consumer

(i) uses Brand B

Let B = event of using Brand B detergent

P(B) = 20055

= 4011

(ii) uses Brand A or Brand D

Let F = event of using Brand A or Brand D

= 200

5040 +

= 20090

= 209

(b) If 1500 consumers were selected from that area, how many would you predict to use Brand C?

Let C = event of using Brand C detergent

P(C) = 20010

= 201

Number of consumers using Brand C detergent = P(C) 1500

= 201

1500

= 75

Mathematics Form 4

1

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Pupils Copy

LESSON 85: Occurrence of an Outcome.

Fill in the empty boxes with the correct answers.

1 A big company wants to give out free advertisement stickers for vehicle owners who drive through one road near its office. To save cost and time, the company wants to estimate the number of cars, lorries and busses that will pass through the road from 9am to 1pm so that the number of stickers to be printed can be determined. So, a survey was done for 1 hour at the road. The following is the result of the survey:

Types of vehicles Cars Lorries Buses Frequency 105 30 15

(a) What is the total number of cars, lorries and busses that passed through the road in that 1 hour?

(b) Estimate the total number of those three vehicles that will pass through that road from 9am to 1pm.

(c) If a vehicle going through the road is selected at random during that 1-hours time, find the probability that the vehicle is

(i) a car. (ii) a bus. (d) If the company is only interested in giving the stickers to owners of cars and

buses only, predict the total number of cars and buses that will pass through the road from 9am to 1pm in a certain day.

2 Mrs. Vijay has invited 500 guests for an evening function. When she ordered 20

samples of cookies for the function to be sent to her, she found that for every 10 cookies, 1 cookie is burnt and hence cannot be served. From 50 invited guests that have replied, 4 of them said that they will not be able to come and 3 of them asked if they can bring a partner, which she consented. (a) If she ordered 1000 of those cookies, predict how many of those cookies

cannot be served because they are burnt. (b) If a guest is randomly chosen from the 50 that has replied, calculate the

probability that the guest will not be able to come to her function. (c) Predict the number of guests that may not be able to come to her function. (d) If a guest is randomly chosen from the 50 that has replied, calculate the

probability that the guest will come with a partner. (e) Predict the number of guests that will come to her function. (f) Hence, determine the minimum number of cookies that she should order so

that every guest who comes to her function will get at least 2 of those cookies. 3 From 15 students that are involved in a science project, 2 of them did not succeed

in completing the project as required. Predict how many would have successfully completed the project if 300 students were involved.

Mathematics Form 4

2

ACTIVITY SHEET

Teachers Copy

LESSON 85: Occurrence of an Outcome.

Fill in the empty boxes with the correct answers.

1 A big company wants to give out free advertisement stickers for vehicle owners who drive through one road near its office. To save cost and time, the company wants to estimate the number of cars, lorries and busses that will pass through the road from 9am to 1pm so that the number of stickers to be printed can be determined. So, a survey was done for 1 hour at the road. The following is the result of the survey:

Types of vehicles Cars Lorries Buses Frequency 105 30 15

(a) What is the total number of cars, lorries and busses that passed through the road in that 1 hour?

(b) Estimate the total number of those three vehicles that will pass through that road from 9am to 1pm.

(c) If a vehicle going through the road is selected at random during that 1-hours time, find the probability that the vehicle is

(i) a car. (ii) a bus. (d) If the company is only interested in giving the stickers to owners of cars and

buses only, predict the total number of cars and buses that will pass through the road from 9am to 1pm in a certain day.

2 Mrs. Vijay has invited 500 guests for an evening function. When she ordered 20

samples of cookies for the function to be sent to her, she found that for every 10 cookies, 1 cookie is burnt and hence cannot be served. From 50 invited guests that have replied, 4 of them said that they will not be able to come and 3 of them asked if they can bring a partner, which she consented. (a) If she ordered 1000 of those cookies, predict how many of those cookies

cannot be served because they are burnt. (b) If a guest is randomly chosen from the 50 that has replied, calculate the

probability that the guest will not be able to come to her function. (c) Predict the number of guests that may not be able to come to her function.

(d) If a guest is randomly chosen from the 50 that has replied, calculate the probability that the guest will come with a partner.

(e) Predict the number of guests that will come to her function. (f) Hence, determine the minimum number of cookies that she should order so

that every guest who comes to her function will get at least 2 of those cookies. 3 From 15 students that are involved in a science project, 2 of them did not succeed

in completing the project as required. Predict how many would have successfully completed the project if 300 students were involved.

150

520

0.7

0.1

416

100

0.08

40

0.06

490

1089

260

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