add maths form 5 chapter 7 probability

Sri Bintang Tuition Centre Additional Mathematics Form 5

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CHAPTER 7: PROBABILITY July 2009

• Probability is a way to describe the possibility of something happening.

For example, when the weather report says that there is a 60% chance of rain today,

that is an expression of probability. And if someone says that you have a 50 − 50

chance of guessing a coin toss - that too, is an expression of probability.

• In general, we say that the probability of something happening is the ratio of the

number of ways that thing can happen to the total number of ways for all things to

happen. The thing we want to happen is usually called the event. So we will need to

know the number of ways for the event to happen and the total number of ways for all

events to happen. In a simpler form,

waysof no total

happen tosomethingfor waysofnumber )( =EP

• Probabilities can only take on values from 0 to 1. Keep in mind that 0 and 1 are

acceptable values for a probability answer. Mathematically this is represented as

0 ≤ P(event) ≤ 1

• A probability of 0 means that an event is impossible and a probability of 1 means that

an event is certain.

For example, for a dice, the probability of rolling a 7 is zero because you can never

roll a 7 with just one dice.

P(7) = 0

Probability of mutually exclusive events or Addition Rule

• The addition rule helps you solve probability problems that involve two events.

• Two events are mutually exclusive if they cannot occur at the same time.

For example, in an experiment where a dice is thrown, the event of obtaining an even

number and the event of obtaining an odd number cannot occur at the same time.

• An event A and an event B are said to be mutually exclusive when:

)()()( BPAPBAP +=∪ or =∩ BA O

• For events not mutually exclusive:

)()()()( BAPBPAPBAP ∩−+=∪

• ∪ means ‘or’.


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Probability of independent events or Multiplication Rule

• Two events are independent if the outcomes of event A do not influence the outcomes

of event B.

For example, suppose we roll one dice followed by another and want to find the

probability of rolling a 4 on the first die and rolling an even number on the second

dice; these two events are independent because their outcomes are not influenced by

each other.

• If events A and B are independent, then

)()()( BPAPBAP ×=∩

• ∩ means ‘and’.

• The concepts of the probability of two independent events can be expanded to three

or more independents events.

• A tree diagram can be constructed to show all the possible outcomes of an

experiment. Each branch shows the possible outcomes of an event.

Examples

1. A letter is randomly selected from the word ‘LIMAU’.

(a) Write down the sample space of this experiment.

(b) Determine the number of possible outcomes of the event that the selected

letter is

(i) a consonant (ii) a vowel.

2. A bag contains 5 red balls, 8 White balls, 4 green balls and 7 black balls. A ball is

drawn at random from the bag. Fine the probability that it is (i) black (ii) not green.

3. There are 25 red marbles and 20 blue marbles in a box. m blue marbles are then

added to the box so that the probability of obtaining a blue marble from the box is

5

4. Calculate the value of m. [Ans: 80]


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4. A number is chosen at random from the sample space, }14,12,10,8,6,4,2{=S . Find

the probability of obtaining a number less than 9 or greater than 11. [Ans: 7

6]

5. In a college, 140 students wear spectacles. If a student is selected randomly, the

probability that the student wears spectacles is 3

1. Later, another 20 students who

wear spectacles join the college. If a student is selected randomly, state the

probability that the student wear spectacles. [Ans: 11

4]

6. Determine whether the following event are mutually exclusive or not.

• A dice is tossed once.

(i) getting an even number and getting an odd number,

(ii) getting a prime number and getting an even number.

7. 8 cards with number from 1 to 8 are placed in a box. A card is picked randomly

from the box.

(a) Is the events of picking an even number and a prime number mutually

exclusive?

(b) Find the probability that the card chosen is

(i) an even number or a prime number,

(ii) an even number and a prime number.

[Ans: (b)(i) 8

7 (ii)

8

1]


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8. A fair coin and a fair dice are thrown simultaneously. Calculate the probability of

obtaining the head of the coin or the number 2 on the dice. [Ans 12

7]

9. Bag A contains four balls numbered 2, 3, 4 and 5. Bag B contains three balls

numbered 3, 4 and 6. A ball is drawn at random from each bag. Calculate the

probability that both balls have the same number or the sum of the numbers on the

two balls is more than 8. [Ans:2

1]

10. Two dice are rolled. Find the probability that the sum of the numbers on the

uppermost face is

(a) an even number or a perfect square.

(b) a perfect square or a number less than 5.

[Ans: (a) 18

11 (b)

4

1]


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11. The probabilities Chong passes his Mathematics, Biology, History test are 0.9, 0.8

and 0.8 respectively. Find the probability that Chong passes all the three subjects. [Ans: 0.576]

12. Two marbles are drawn at random from the box which contains 5 black marbles, 3

yellow marbles and 2 white marbles. Find the probability that the yellow and black

marbles are obtained. [Ans: 6

1]

13. A fair dice and a fair coin are tossed once each. Find the probability that

(a) an even number on the dice and a heads on the coin is obtained,

(b) a multiple of three and a tails is obtained.

[Ans: (a) 4

1 (b)

6

1]

14. Given that the probability that the soldier hitting the target in each shot is 0.9. If the

soldier fires three shots in succession, find the probability that the soldier hits the

target twice. [Ans: 0.243]


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15. Alan, Chai and Daud take an exam and the probabilities that they pass are 3

2,

2

1 and

4

3 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.

[Ans: (a) 4

1 (b)

24

17 (c)

24

23]

16. There are 50 students in a class, of whom 10 are left-handed. Two students are

selected at random. What is the probability that

(a) both are right-handed,

(b) both are left-handed,

(c) one is left-handed and the other is right-handed.

[Ans: (a) 245

156 (b)

245

9 (c)

49

16]

add maths form 5 chapter 7 probability

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