les4e_ppt_ch03 [Compatibility Mode]

les4e_ppt_ch03 [Compatibility Mode] - Chapter 3 Chapter 3...

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Chapter 3 Larson/Farber 4 th ed 1 Chapter 3 Probability Larson/Farber 4th ed 1 Chapter Outline 3.1 Basic Concepts of Probability 3.2 Conditional Probability and the Multiplication Rule 3.3 The Addition Rule 3.4 Additional Topics in Probability and Counting Larson/Farber 4th ed 2
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Chapter 3 Larson/Farber 4 th ed 2 Section 3.1 Basic Concepts of Probability Larson/Farber 4th ed 3 Section 3.1 Objectives Identify the sample space of a probability experiment Identify simple events Use the Fundamental Counting Principle Distinguish among classical probability, empirical probability, and subjective probability Determine the probability of the complement of an event Use a tree diagram and the Fundamental Counting Principle to find probabilities Larson/Farber 4th ed 4
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Chapter 3 Larson/Farber 4 th ed 3 Probability Experiments Probability experiment An action, or trial, through which specific results (counts, measurements, or responses) are obtained. Outcome The result of a single trial in a probability experiment. Sample Space The set of all possible outcomes of a probability experiment. Event Consists of one or more outcomes and is a subset of the sample space. Larson/Farber 4th ed 5 Probability Experiments Probability experiment: Roll a die Outcome: {3} Sample space: {1, 2, 3, 4, 5, 6} Event: {Die is even}={2, 4, 6} Larson/Farber 4th ed 6
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Chapter 3 Larson/Farber 4 th ed 4 Example: Identifying the Sample Space A probability experiment consists of tossing a coin and then rolling a six sided die Describe the sample space then rolling a six-sided die. Describe the sample space. Solution: There are two possible outcomes when tossing a coin: a head (H) or a tail (T). For each of these, there are six possible outcomes when rolling a die: 1 2 3 4 5 or Larson/Farber 4th ed 7 possible outcomes when rolling a die: 1, 2, 3, 4, 5, or 6. One way to list outcomes for actions occurring in a sequence is to use a tree diagram. Solution: Identifying the Sample Space Tree diagram: H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6 Larson/Farber 4th ed 8 The sample space has 12 outcomes: {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
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Chapter 3 Larson/Farber 4 th ed 5 Simple Events Simple event An event that consists of a single outcome. ± e.g. “Tossing heads and rolling a 3” {H3} An event that consists of more than one outcome is not a simple event. ± e.g. “Tossing heads and rolling an even number” {H2, H4, H6} Larson/Farber 4th ed 9 Example: Identifying Simple Events Determine whether the event is simple or not. You roll a six-sided die. Event B is rolling at least a 4. Solution: Not simple (event B has three outcomes: rolling a 4, a 5, or a 6) Larson/Farber 4th ed 10
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Chapter 3 Larson/Farber 4 th ed 6 Fundamental Counting Principle Fundamental Counting Principle If one event can occur in m ways and a second event can occur in n ways, the number of ways the two events can occur in sequence is m*n .
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les4e_ppt_ch03 [Compatibility Mode] - Chapter 3 Chapter 3...

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