16/4/1435 h Sunday
Lecture 2 Sample Space and Events
Jan 2009 1
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
Jan 2009 2
.C. Three times
= 23 = 8 elements
2. Roll a fair die: A. Once:
= 61 = 6 elements
B. Twice:
= 62 = 36 elements
Jan 2009 3
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}
Jan 2009 5
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}
Jan 2009 6
.
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
.
Jan 2009 8
.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,)}
Jan 2009 9
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)}
Jan 2009 10
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 }
Jan 2009 11
.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, …}
Jan 2009 12