CHAPTER 7 PROBABILITY I

Lydia TwinNor IzzatiNashasha NabilaSaidatuna Miftahul Jannah

Subtopic

7.1 Concept of sample space

7.2 Concept of events

7.3 Use the concept of probability of an event to

solve problems

7.1 The Concept Of Sample Space

Learning Outcomes:Students are able to:-• Determine whether an outcome is a possible

outcome of an experiment• List all the possible outcomes of an experiment– From activities;– By reasoning

• Determine the sample space of an experiment• Write the sample space by using set notation

Learning outcome 1

a) Determine whether an outcome is a possible outcome of an experiment

Example 1: Determine whether the following are the possible outcome when tossing a 10 sen and 50 sen coin

Case 1: Tossing a 10 sen coinI) A symbol of 10 sen II) A picture of a wauIII) A symbol of 50 sen IV) A picture of congkak

Cont…

Case 2: Tossing a 50 sen coinI) A symbol of 20 sen II) A picture of a wauIII) A picture of congkakIV) A symbol of 50 sen

TRY THIS:A pouch contains orange, green, yellow and white coloured chips. If a chip is taken out at random, determine whether the following outcomes are possible.a) Getting a red chipb) Getting a green chipc) Getting a orange chipd) Getting a blue chipe) Getting a yellow chip

TRY THIS:A pouch contains orange, green, yellow and white coloured chips. If a chip is taken out at random, determine whether the following outcomes are possible.a) Getting a red chipb) Getting a green chipc) Getting a orange chipd) Getting a blue chipe) Getting a yellow chip

Learning outcome 2

b) Determine the possible outcomes of an experiment

From activities By reason

Example 2: A card is drawn from a set of cards written the letters R,E,S,P,E,C and T. Write down all the possible outcomes by reasoning.

R E S P E C T

ACTIVITY!!• Take out a coloured love paper from a

small box that containing 3 red, 4 blue and 2 green love papers.

– Use Tree Diagram, write down all the possible outcomes if 2 coloured love papers are taken out randomly.

Learning outcome 3

c) Determine the sample space of an experiment and write it by set notation

Set of possible outcomes, S={ } Sample Space, S={ }

Example 3: State the sample space by using set notation when i) a dice is rolled.ii) Two die are rollediii) Two cards are picked randomly, one at the time,

from three cards labelled with 1,2 and 3. Write the possible outcomes if:-

1. Without returning the first card.2. Returning the first card after it is drawn

Solutions to Examples

Example 1

Question:Case 1: Tossing a 10 sen I) A symbol of 10 sen

-->II) A picture of a wau

-->III) A symbol of 50 sen

-->IV) A picture of congkak

-->

Answer

Possible outcomesI) PossibleII) Not PossibleIII) Not PossibleIV) Possible

Example 1

Question:Case 2: Tossing a 50 sen I) A symbol of 20 sen

-->II) A picture of a wau

-->III) A picture of congkak

-->IV) A symbol of 50 sen

-->

Answer

Possible outcomesI) Not PossibleII) PossibleIII) Not PossibleIV) Possible

TRY THIS:

A pouch contains orange, green, yellow and white coloured chips. If a chip is taken out at random, determine whether the following outcomes are possible.a) Getting a red chip Not Possibleb) Getting a green chip Possiblec) Getting a orange chip Possibled) Getting a blue chip Not Possiblee) Getting a yellow chip Possible

Example 2

Question:

A card is drawn from a set of cards written the letters R,E,S,P,E,C and T. Write down all the possible outcomes by reasoning.

Answer:Possible outcomes: R, E, S, P, C, TWhy? Since we have 2 cards of letter E,

we just take one of them.

R E S P E C T

Example 3Answer:i) A dice is rolledS= {1, 2, 3, 4, 5, 6}

ii) Two die are rolledS={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6), (5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

iii) 1. Without returning the first cardS={(1,2),(1,3),(2,1),(2,3),(3,1),(3,2)}

2. Returning the first card after it is drawnS={(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)}

7.2 CONCEPT OF AN EVENT

EVENT

Is one or more outcomes of the experiment that satisfy certain conditions.

A subset of the sample space

7.2a Identify the elements of a sample space which satisfy given

conditions

EXAMPLE: A box has 6 yellow marbles and 4 green marbles. If two marbles are picked, write down the elements of sample space

SOLUTION

S = { GY , YG}

Where, G – green Y – yellow

7.2b Elements of a sample space which satisfy certain conditions using set notation

Example: Given element of sample space,

S = (1,1) , (2,2) , (3,3)Written using set notation,

P = { (1,1) , (2,2) , (3,3) }

P is a subset of S

7.2c Determine whether an event is possible for a sample space

I) Event P is the event of getting number 4

= possible

ii) Event Q is the event of getting blue card of number 3 = impossible

iii) Event R is the event of getting yellow card of number 1 = possible

7.3.USE OF PROBABILITY OF AN

EVENT TO SOLVE PROBLEMS.Mathematics is FUN!=)

Probability of an event A is :

P(A)=Number of times event A occur

Numbers of trial

Find the ratio of the number of times an event occurs to the

numbers of trials.

If P(A)=O, then A will not occur.If P(A)=1 , then A will occur in

every trial.

Therefore, for all the event, 0≤P(A)≥1

7.3b. Find the probability of an event from a big enough numbers of trials.

By using the given formula in above, solve this questions.

Type of game

softball Swimming

Badminton

Squash

Number of student

550 250 350 150

Find the probability that the selected student likes.

a) Softball b) badminton

TRY IT !! =)

a)P(selected student likes softball)

b) P(selected student like badminton)

SOLUTIONS,,,,,

5501300

=1126

3501300

=726

7.3c. Find expected number of times an event will occur, given the probability of the event and number of trials

At previous section, you have know that the probability of the event A Is:

P(A)= Number of times event A occur Number of trials

So, if we are given the probability of the event and the number of trials,we can find the number of times an event will occur which is:

Number of times an event A occur = P(A)X Number of trials.

TRY THIS….The probability to get red marble in a box is 0,8. If there is 200 marble inside the box, What is the number of red marble .Number of red marble= P(A) x number of marble=0.8 x200=160 Help me solve

this problem…..

Probability also being apply in real life

problem. You can use the previous learning to solve the

problem.

7.3d Solve problems involving probability

A survey is made on the mean of school

transport by student in SMK Jasa Murni.The data obtained is shown in the table below.

TRY THIS PROBLEM…

Means of transport

School bus bicycle Other means

Number of student

700 200 200

If a student from a school is randomly picked, what is the probability that the student goes to school by:a) School busb) Bicyclec) Other mean of transport.

SoLuTiOns:

Total student= 700 +200 +200 =1100

a)P(By school bus)=700/1100=7/11=0.64

b)P(by bicycle)=200/1100=2/11=0.18

c)P(by others )=200/1100=2/11=0.18

THE

Good luck everyone

END…