16/4/1435 h Sunday

Lecture 2 Sample Space and Events

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Number of Elements in a Sample SpaceNumber of elements in = number of elements inn

a sample space a sample space in one experimentWhere: n is a number of time the experiment is

repeatedExamples:1.Toss a coinA.Once

= 21 =2 elementsB.Twice

= 22 =4 elements

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.C. Three times

= 23 = 8 elements

2. Roll a fair die: A. Once:

= 61 = 6 elements

B. Twice:

= 62 = 36 elements

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1. Sample Space and Events For Simple Events

1.Roll a die Once

A six-sided die has this sample spaceNumber of elements in the sample space =

= 61= 6 elements

Sample space:

S = {1, 2, 3, 4, 5, 6}Simple events (or outcomes):

E1= {1} , E2 = {2} , E3 = {3} E4 = {4}

E5 = {5} E6 = {6} 4

2. Toss a coin once Q: Show the sample space Sample space: Number of elements in the

sample space =

= 21 = 2

Where: H = Head T = Tail Simple events (or outcomes):E1( Head) = {H}E2(Tail} = {T}

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THS ,

02. Sample Space and Events For Compound Events

3. Roll a dieQ: Observe these eventsA: odd numbers A = {1, 3, 5}B: observe an even number B= {2, 4, 6}C: observe a number greater than or

equal to 4 C= {4, 5, 6}D: observe a number less than or

equal to 4 D = {4, 3, 2,1}

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.

2. The roll of a Two diceQ: Show the sample space when two

unbiased dice were rolled or (if one die is rolled twice)

Number of elements in the sample space =

= 62 = 36 elements

.

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.Examples that shows compound

events of rolling two dice:Q: show the event of Sum of 6A: = { (1,5),(5,1),(2,4),(4,2),(3,3)}Q: show the event that shows similar

faces B= {(1,1),(2,2),(3,3),(4,4),(5,5),

(6,6,)}

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3.Toss a coin twice Q:Show the sample space?The number of elements in the sample space

= 22 = 4 elements

Show these events:A: Observe the number of heads A = { 0, 1, 2, }B : Having exactly two head B={(H,H)}C: Having at least one headC = {(H,H),(H,T),(T,H)}

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TTHTTHHHS ,,,,,,,,

.D: Observe the number of tails

D = { 0, 1, 2, }

E: Having exactly two tail

E={(T,T)}

F: Having at least one tail

F = {(T,T),(H,T),(T,H)}

4. Toss a coin three timesQ: Show the sample space

The number of elements in the sample space

= 23 = 8 elementsS={(H,H,H),(H,H,T),(H,T,H),(T,H,H),(H,T,T),(T,H,T),(T,T,H),

(T,T,T)}

Q: Observe the number of heads

S = { 0, 1, 2,3 }

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.Q: Observe these events

A: number of Tails A = { 0, 1, 2,3 }

B: Having at least one headB={(T,H,T), (H,T,T),(T,T,H), (H,T,H),(T,H,H), (H,H,T),(H,H,H),}

C: Show the sample space that represents the working state of a machine

C = { working, fail }D: Show the sample space that represents the number of

calls arriving at a telephone exchange during a specific time interval

D = { 0, 1, …}

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