Probability Sample Spaces Assigning Probability Conclusion MATH 105: Finite Mathematics 7-1: Sample Spaces and Assignment of Probability Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006
Probability Sample Spaces Assigning Probability Conclusion Outline Probability 1 Sample Spaces 2 Assigning Probability 3 Conclusion 4
Probability Sample Spaces Assigning Probability Conclusion Outline Probability 1 Sample Spaces 2 Assigning Probability 3 Conclusion 4
Probability Sample Spaces Assigning Probability Conclusion Introduction to Probability Many real world events can be considered chance or random. They may be deterministic, but we can not know or comprehend all the factors which determine the outcome. Example You flip a coin. Air current, the arrangement of the coin on your finger, the force of your flip, and other factors all go together to determine the outcome of Heads or Tails. For any one toss, these factors are too complicated to take into account, and the outcome appears random. Since the outcome is heads roughly half the time, we assign the following probabilities: Pr [ H ] = 1 Pr [ T ] = 1 2 2
Probability Sample Spaces Assigning Probability Conclusion Introduction to Probability Many real world events can be considered chance or random. They may be deterministic, but we can not know or comprehend all the factors which determine the outcome. Example You flip a coin. Air current, the arrangement of the coin on your finger, the force of your flip, and other factors all go together to determine the outcome of Heads or Tails. For any one toss, these factors are too complicated to take into account, and the outcome appears random. Since the outcome is heads roughly half the time, we assign the following probabilities: Pr [ H ] = 1 Pr [ T ] = 1 2 2
Probability Sample Spaces Assigning Probability Conclusion Probability Vocabulary Probability Terms Outcome A particular result of an activity or event. Event A set of outcomes which share a common characteristic. Sample Space The set of all possible outcomes for an experiment. This is the universal set for the experiment. Equally Likely Events All events in the sample space have the same probability.
Probability Sample Spaces Assigning Probability Conclusion Probability Vocabulary Probability Terms Outcome A particular result of an activity or event. Event A set of outcomes which share a common characteristic. Sample Space The set of all possible outcomes for an experiment. This is the universal set for the experiment. Equally Likely Events All events in the sample space have the same probability.
Probability Sample Spaces Assigning Probability Conclusion Probability Vocabulary Probability Terms Outcome A particular result of an activity or event. Event A set of outcomes which share a common characteristic. Sample Space The set of all possible outcomes for an experiment. This is the universal set for the experiment. Equally Likely Events All events in the sample space have the same probability.
Probability Sample Spaces Assigning Probability Conclusion Probability Vocabulary Probability Terms Outcome A particular result of an activity or event. Event A set of outcomes which share a common characteristic. Sample Space The set of all possible outcomes for an experiment. This is the universal set for the experiment. Equally Likely Events All events in the sample space have the same probability.
Probability Sample Spaces Assigning Probability Conclusion Probability Vocabulary Probability Terms Outcome A particular result of an activity or event. Event A set of outcomes which share a common characteristic. Sample Space The set of all possible outcomes for an experiment. This is the universal set for the experiment. Equally Likely Events All events in the sample space have the same probability.
Probability Sample Spaces Assigning Probability Conclusion Outline Probability 1 Sample Spaces 2 Assigning Probability 3 Conclusion 4
Probability Sample Spaces Assigning Probability Conclusion Finding Sample Spaces One of the first tasks in finding probability is to determine the sample space for the experiment. Example You flip a fair coin. What is the sample space for this experiment? Example You roll a six-sided die and note the number which appears on top. What is the sample space for this experiment?
Probability Sample Spaces Assigning Probability Conclusion Finding Sample Spaces One of the first tasks in finding probability is to determine the sample space for the experiment. Example You flip a fair coin. What is the sample space for this experiment? Example You roll a six-sided die and note the number which appears on top. What is the sample space for this experiment?
Probability Sample Spaces Assigning Probability Conclusion Finding Sample Spaces One of the first tasks in finding probability is to determine the sample space for the experiment. Example You flip a fair coin. What is the sample space for this experiment? S = { H , T } Example You roll a six-sided die and note the number which appears on top. What is the sample space for this experiment?
Probability Sample Spaces Assigning Probability Conclusion Finding Sample Spaces One of the first tasks in finding probability is to determine the sample space for the experiment. Example You flip a fair coin. What is the sample space for this experiment? S = { H , T } Example You roll a six-sided die and note the number which appears on top. What is the sample space for this experiment?
Probability Sample Spaces Assigning Probability Conclusion Finding Sample Spaces One of the first tasks in finding probability is to determine the sample space for the experiment. Example You flip a fair coin. What is the sample space for this experiment? S = { H , T } Example You roll a six-sided die and note the number which appears on top. What is the sample space for this experiment? S = { 1 , 2 , 3 , 4 , 5 , 6 }
Probability Sample Spaces Assigning Probability Conclusion Finding More Sample Spaces Example You flip a coin and roll a die, and note the result of each. what is the sample space for this experiment? S = { H 1 , H 2 , . . ., H 6 , T 1 , T 2 , . . ., T 6 } c ( S ) = 2 · 6 = 12
Probability Sample Spaces Assigning Probability Conclusion Finding More Sample Spaces Example You flip a coin and roll a die, and note the result of each. what is the sample space for this experiment? S = { H 1 , H 2 , . . ., H 6 , T 1 , T 2 , . . ., T 6 } c ( S ) = 2 · 6 = 12
Probability Sample Spaces Assigning Probability Conclusion Finding More Sample Spaces Example You flip a coin and roll a die, and note the result of each. what is the sample space for this experiment? S = { H 1 , H 2 , . . ., H 6 , T 1 , T 2 , . . ., T 6 } c ( S ) = 2 · 6 = 12
Probability Sample Spaces Assigning Probability Conclusion Different Sample Spaces for the Same Experiment Example You roll two dice and note both numbers. What is the sample space for this experiment? Example You roll two dice and note the sum of the two numbers. What is the sample space for this experiment?
Probability Sample Spaces Assigning Probability Conclusion Different Sample Spaces for the Same Experiment Example You roll two dice and note both numbers. What is the sample space for this experiment? S = { (1 , 1) , (1 , 2) , . . ., (2 , 1) , (2 , 2) , . . . } c ( S ) = 6 · 6 = 36 Example You roll two dice and note the sum of the two numbers. What is the sample space for this experiment?
Probability Sample Spaces Assigning Probability Conclusion Different Sample Spaces for the Same Experiment Example You roll two dice and note both numbers. What is the sample space for this experiment? S = { (1 , 1) , (1 , 2) , . . ., (2 , 1) , (2 , 2) , . . . } c ( S ) = 6 · 6 = 36 Example You roll two dice and note the sum of the two numbers. What is the sample space for this experiment?
Probability Sample Spaces Assigning Probability Conclusion Different Sample Spaces for the Same Experiment Example You roll two dice and note both numbers. What is the sample space for this experiment? S = { (1 , 1) , (1 , 2) , . . ., (2 , 1) , (2 , 2) , . . . } c ( S ) = 6 · 6 = 36 Example You roll two dice and note the sum of the two numbers. What is the sample space for this experiment? S = { 2 , 3 , . . ., 12 } c ( S ) = 11
Probability Sample Spaces Assigning Probability Conclusion Taking a Quiz Example You take a True/False quiz with three questions. If you treat this quiz as an experiment, what is the sample space?
Probability Sample Spaces Assigning Probability Conclusion Taking a Quiz Example You take a True/False quiz with three questions. If you treat this quiz as an experiment, what is the sample space? S = { TTT , TTF , . . ., FFF } c ( S ) = 8
Probability Sample Spaces Assigning Probability Conclusion Taking a Quiz Example You take a True/False quiz with three questions. If you treat this quiz as an experiment, what is the sample space? S = { TTT , TTF , . . ., FFF } c ( S ) = 8 Now that we have some practice identifying sample spaces, it is time to start assigning probabilities.
Probability Sample Spaces Assigning Probability Conclusion Outline Probability 1 Sample Spaces 2 Assigning Probability 3 Conclusion 4
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