My

AdditionalMathematic

sModules

Form 5

Topic: 1

Name : __________________________

Class : 5 ____________

Additional Mathematics Form 5: Chapter 7 Probability

My

AdditionalMathematic

sModules

Form 5

Topic: 1

Name : __________________________

Class : 5 ____________

7.1 Probability 1. A bag contains 8 red pens and 6 blue pens. Find the

probability that a pen, randomly selected from the bag, is a blue pen.

2. A fair dice is rolled once. Find the probability that the result is an even number.

3. A letter is chosen from the word UNIVERSAL. Find the probability that the letter is a vowel.

4. Twenty cards, numbered from 21 to 40, are put in a bag. A card is drawn randomly from the bag. Find the probability that the number on the card is a prime number.

5. A box contains 4 red, 5 black and 6 blue marbles. If a marble is drawn randomly from the box, find the probability that the marble is blue.

6. P R O B A B I L I T Y

The letters of the word PROBABILITY are written on eleven cards. If one card is drawn at random, what is the probability that the card has(a) the letter B?(b) a vowel?

7. A bag contains 9 balls, numbered from 1 to 9. Aziz draws a ball randomly from the bag. Find the probability that the number on the ball is(a) an odd and primer number,(b) an odd or prime number.

8. A box contains cards, numbered from 20 to 30. Ah Mei chooses a card randomly from the box. Find the probability that the number on the card is(a) an even number and a multiple of 3.(b) An even number or a multiple of 3.

9. There are forty students in a class. Given that 18 of them like to play football, 25 of them like to play badminton and 8 of them like to play both games. If a student is randomly selected from the class, find the probability that the student likes to play(a) football and badminton,(b) football or badminton.

10. Johan selects a number from set S, where S=

Determine the

probability that the number obtained is (a) a multiple of 3 and 5(b) a multiple of 3 or 5

7.2 Probability of Mutually Exclusive Events

1. A fair six-sided dice is rolled. Find the probability of obtaining(a) the number 2 or 3,(b) an even number or the number 3.

2. A bag contains 4 red, 5 blue and 6 yellow marbles. A marble is drawn randomly from the bag. Find the probability that the colour of the marble is(a) red or blue(b) rexd or yellow.

1. The sample space, S, is a set of all the possible outcomes of an experiment. 2. An event is a subset of the sample space which satisfies certain conditions.

3. The probability that an even A occurs is .

4. The probability that an event A does not occur is .

5. The probability that event A or B occurs is .

1. Two events A and B are mutually exclusive if both events cannot occur at the same time, .

2. The probability that event A or B occurs is .

3. Nine cards are written with the letters of the word STATISTIC. If a card is selected randomly, find the probability that the card has the letter(a) I or T(b) T or a vowel

4. Muthu chooses a number randomly from a set S, where S=

. Find the probability

that the number is(a) an even or prime number(b) a prime number or a multiple of 5

7.3 Probability of Independent Events

1. Ai Leng tossed a coin and a dice simultaneously. Find the probability of obtaining a heads and the number 3.

2. The probabilities of Sunny winning in the Science quiz and

Mathematic quiz are and respectively. Find the

probability that he will win in both quizzes.

3. The probability that a shooter hits the target is . What is

the probability that he will hit the target every time if he fires 3 times?

4. The probabilities for Rashid and Prakash to be present in a

badminton tournament are and respectively. Find the

probability that(a) both of them are present(b) only one of them is present

5. Bag A contains 3 red and 4 green balls. Bag B contains 6 red and 2 green balls. If a ball is drawn from each bag, find the probability that (a) both of the balls are red(b) the ball from bag A is red and the ball from bag B is

green.

6. The are ten clocks in a box. Four of them are spoilt. If two clocks are drawn, one by one, from the box, find the probability that(a) both clocks are in good condition(b) one clock is spoilt

7. The probability of obtaining a spoilt orange from a basket

is . If three oranges are selected, find the probability

that(a) all the three oranges are spoilt(b) only one orange is spoilt

8. A fair dice is rolled three time. Find the probability that(a) the number 6 is obtained three times(b) the number 6 is obtained only once

1. Two events, A and B, are independent if the probability that event A occurs does not depend on the outcome of event B, and vice versa.

2. The probability that events A and B occur is

9. In a shooting session, the probabilities of Albert, Basir and

Chandran hitting the target are , and respectively. If

they shoot simultaneously, find the probability that(a) all three of them hit the target(b) only one of the hits the target.

10. In a certain region, its rains on two days a week. Find the probability that on 3 particular days,(a) it rains for 3 days(b) it rains for only 2 days

11. Yunus and Zul are competing in a tennis tournament. The game will end when any player wins 3 sets. The probability

that Yunus wins in any set is .Calculate the probability

that Yunus will win after playing 4 sets.

12. Ester, Fatimah and Gan are sitting for a qualifying test together. The probabilities of Ester, Fatimah and Gan passing the test are 0.5, 0.6 and 0.3 respectively. Calculate the probability that at least one of them pass the test.

13. In a certain area, the probability that its rains on Saturday

is , but the probability that it rains on Sunday is .

Calculate the probability that it rains on any one day.

14. A box contains 4 red, 5 green and 6 yellow marbles. If three marbles are drawn randomly from the box, find the probability that all the three marbles have different colours.

15. A bag contains 4 red balls, 3 green balls and 5 yellow balls. A ball is taken from the bag at random. After record its colour, it is returned into the bag. Then, a second ball is taken. Find the probability that(a) the colour is yellow for both times(b) the first time is red and the second time it is green

Students

Mathematic

Science

A

5

4

B

16. The table shows the probabilities of two students A and B in passing their two subjects Mathematics and Science in an examination. If both of them take the examination, find the probability that(a) A will pass in both subjects(b) B will pass in Mathematics only(c) A will fail in both subjects.

17. A bag contain 5 re cards and 2 yellow cards. Two cards are chosen, one after another, at random. Find the probability that(a) they are both red(b) they are of different colours

18. The probability that a candidate passing the Physics

examination is and that of passing Chemistry is .

What is the probability that he passes one of the examinations?

19. SPM2004/1/24(3 marks) A box contains 6 white marbles and k black marbles. If a marble is picked randomly from the box, the probability of

20. SPM2005/1/25 (3 marks)

The table shows the number of coloured cards in a box.

Colour Number of cards

getting a black marble is .

Find the value of k.

Black 5Blue 4Yellow 3

Two cards are draw at random from the box. Find the probability that both cards are of the same colour.

21. SPM2006/1/23 (3 marks) The probability that Hamid qualifies for the final of a track

event is while the probability that Mohan qualifies is .

Find the probability that(a) both of them qualify for the final,(b) only one of them qualifies for the final.

22. SPM 2008/1/24(4 marks) The probability of Sarah being chosen as a school prefect

is while the probability of Aini being chosen is .

Find the probability that(a) neither of them is chosen as a school prefect,(b) only one of them is chosen as school prefect.

23. SPM2009/P1/23(4 marks) The probability that a student is a librarian is 0.2. Three students are chosen at random. Find the probability that(a) all three are librarians.(b) Only one of them is a librarian.

24. SPM1998/2/10(b) Rashid plays Rudi in a badminton match. The match ends when one of them wins two sets. The probability that Rashid

will win in any of the sets is . Find the probability that

(a) the match ends with 2 sets only,(b) Rashid won the match after playing 3 sets.

25. SPM1996/2/9(a) Kevin wants to buy a television and a refrigerator from a shop that has 5 televisions P, Q, R, S and T and 4 refrigerators W, X, Y and Z. Calculate the probability that television P or Q and refrigerator W are chosen.

26. SPM1980/1/23Mathematic

sGeography

Hamzah

Roslan

The table shows the probability of Hamzah and Roslan in passing their two subjects Mathematics and Geography in an examination. If both of the take the examination, find the probability that

(a) Roslan will pass in both subjects,(b) Hamzah will pass in Mathematics only,(c) Each of them will pass one subject only,

27. Alan, Benson and Carmen take an exam and the

probability that they pass are , and respectively.

Calculate the probability that(a) only one of them passes the exam,(b) at least two of them pass the exam,(c) at least one of them passes the exam.

28. Given that the probability of Alan passing the subjects

Physics, Chemistry and Biology are , and

respectively. What is the probability that(a) he passes all the three subjects,(b) he passes only two subjects.

29. GCE O Level N001I/D A bag contains 3 black and 2 white balls. Two balls are taken from the bag at random, without replacement. By drawing a tree diagram, or otherwise, calculate the probability that,

(a) both balls are black,(b) at least one ball is white,(c) two balls are the same colour.

30. GCE O Level J94I/D A bag contains 6 red sweets, 3 yellow sweets and 1 green sweet. Two sweets are drawn at random from the bag, one after other, and are not replacement. Find the probability that(a) the first sweet taken is red,(b) both the sweets are red,(c) both of the sweets are the same colour,(d) the two sweets are different colours.

31. GCE O Level N94I/D A teacher(T), 3 boys(B) and 4 girls(G) are on a school committee. Two representative are selected at random from the committee. Calculate the probability that(a) both representative are girls,(b) the representatives are not both girls,(c) one representative is a boy and the other a girl.

32. SPM1983/2/23(a) Two fair dice are tossed. Find the probability that (a) sum of the scores are greater than 4,(b) product of the scores is an odd number,(c) product of the score is a multiple of 3.

33. The probability that it rains on any day is . Out of two

consecutive days, calculate the probability that it rains on at least one day.

34. In an archery competition, the probability that Mr. Raju

and Mr. Tan will qualify for the final is and

respectively. Find the probability that(a) both of them fail to qualify for the final,(b) one of them fail to qualify for the final.

35. SPM1981/2/8 Box A contain 5 similar cards labeled with the numbers 1,3,5,7 and 9, whereas box B contains 3 similar cards labelled with the numbers 1,4 and 9. A card is chosen randomly from box A and box B respectively. Find the probability that the numbers taken from the two boxes

(a) has the same numbers,(b) has a sum which is greater than 3,(c) has a product which is divisible by 3.

36. SPM2000/2/9 Box A contain 4 similar balls labeled with the numbers 1,2,3 and 4, whereas box B contains 3 similar balls labeled with the numbers 2,3 and 5. A ball is chosen randomly from box A and box B respectively. Find the probability that the numbers taken from the two boxes(a) has the same numbers,(b) has the sum does not exceed 5.

37. SPM2010/1/24(3 marks) In a selection of a class monitor, the probability that

student X is chosen is , while the probability that either

student X or student Y is chosen is . Find the probability

that(a) student Y is chosen,(b) student X or student Y is not chosen.

38. SPM2011/1/24(3 marks) A sample space of an experiment is given by S = { 1, 2, 3, …, 20}. Events M and N are defined as follows:M: {3, 6, 9, 12, 15, 18 }N : { 1, 3, 5, 15 }

Find(a) P(M)(b) P(M and N)