1. 16/4/1435 h Sunday Lecture 2 Sample Space and Events Jan 2009 1

2. Number of Elements in a Sample Space Number of elements in = number of elements in n a sample space a sample space in one experiment Where: n is a number of time the experiment is repeated Examples: 1. Toss a coin A. Once = 2 1 =2 elements B. Twice = 2 2 =4 elements Jan 2009 2

3. . C. Three times = 2 3 = 8 elements 2. Roll a fair die: A. Once: = 6 1 = 6 elements B. Twice: = 6 2 = 36 elements Jan 2009 3

4. 1.Sample Space and Events For Simple Events 1.Roll a die Once A six-sided die has this sample space Number of elements in the sample space = = 6 1 = 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

5. 2.Toss a coin once Q: Show the sample space  Sample space: Number of elements in the sample space = = 2 1 = 2 Where: H = Head T = Tail  Simple events (or outcomes): E1( Head) = {H} E2(Tail} = {T} Jan 2009 5

6. 0 2. Sample Space and Events For Compound Events 1. Roll a die Q: Observe these events A: 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

7. . 2. The roll of a Two dice Q: Show the sample space when two unbiased dice were rolled or (if one die is rolled twice) Number of elements in the sample space = = 6 2 = 36 elements

8. . Jan 2009 8

9. . Examples that shows compound events of rolling two dice: Q: show the event of Sum of 6 A: = { (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

10. 3.Toss a coin twice Q:Show the sample space? The number of elements in the sample space = 2 2 = 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 head C = {(H,H),(H,T),(T,H)} Jan 2009 10

11. . 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 times Q: Show the sample space The number of elements in the sample space = 2 3 = 8 elements S={(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

12. . Q: Observe these events A: number of Tails A = { 0, 1, 2,3 } B: Having at least one head B={(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 n umber of calls arriving at a telephone exchange during a specific time interval D = { 0, 1, …} Jan 2009 12