By.Risal Nabas

SAMPLE SPACE

Mathematic Grade XISemester I (odd

Semester)

Preview

Purpose

Material Example Exercise Competence test

Question : What is the meaning of sample space, point, event of sample space of an experiment?

Ilustration

Material Example Exercise Competence test

• Sample space is set possible outcomes of an experiment.

• Sample point is each elements that included in sample space set

• Number/ size (n(s)) is number/quantity of all element that included in sample space

• Event is any arbitrary subset that included in sample space

Concept

Material Example Exercise Competence test

Example

1. Two coins is tossed together, determine the sample space and size of sample space?

2. One red dice and one white dice is tossed together once, determine sample space and size sample space of the experiment?

And then if X is event getting sum of two die/score is 10, determine elements of X !

Material Example Exercise Competence test

Solution of number 1

• Sample Space (S) : {NN, NP, PN, PP}• Size of Sample Space n(S) = 4

Coin I Coin II

NNNP

PNPP

Material Example Exercise Competence test

Solution of number2

 Red dies

1 2 3 4 5 6

White dies

1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

2 (2,1)

3 (3,1)

4 (4,1)

5 (5,1)

6 (6,1)

Material Example Exercise Competence test

Solution of number2

• Sample space:• Size of sample space is n (S) =

• X =

 Red dies

1 2 3 4 5 6

White dies

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)

{(1,1), (1,2), (1,3), . . .(6,6)}36

{(4,6),(5,5),(6,4)}X is event getting sum of two die/score is 10

Material Example Exercise Competence test

1.Determine sample space and size of sample space of the experiment: a. Three coins is tossed together.

b. A coin and a dice is tossed together2.Determine X and how many elements ofX :

a. X is event getting even score of experiment a dice is tossed

b. X is event getting side same by simultaneity in two coins is tossed

Exercise

Material Example Exercise Competence test

Solution exercise Number 1. a

N

PNP

NP

NNNNNPNPNNPP

• Sample Space is : {NNN, NNP, . . . PPP}• Size of sample space is n (S) = 8

NP

NP

NP

NP

PNNPNPPPNPPP

Material Example Exercise Competence test

Solution exercise Number 1. b

• Sample Space : {(N,1), (N,2), (N,3), . . .(P,6)}• Size of sample space is n (S) = 12

 

Dies

1 2 3 4 5 6

Coin N (N,1) (N,2) (N,3) (N,4) (N,5) (A,6)

P (P,1) (P,2) (P,3) (P,4) (P,5) (P,6)

Material Example Exercise Competence test

Solution exercise Number 2

a. Sample space : {1, 2, 3, 4, 5, 6}X is event getting even score of

experiment a dice is tossed X = {2, 4, 6}

b. Sample space: {NN, NP, PN, PP}X is event getting side same by

simultaneity in two coins is tossed.

X = {NN , PP}

Material Example Exercise Competence test

3 ways to determine sample space of an example : • By direct record

(like ilustration 1 and ilustration 2) • By tree shcema

(like solution of example number 1) • By Table

(like solution of example number 2)

To memorize

Material Example Exercise Competence test

Competence test

Purpose of Competence test is to measure achievement of students about “determine sample space of an experiment”.

Competence test such as 5 multiple choise test, and use

Quiz Creator. Document of competence

test.

Material Example Exercise Competence test

If you want to repeat at home, the

material can you get in FB: WTA for SULUT