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notes515fall10chap3 - STAT 515 - Chapter 3: Probability...

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STAT 515 --- Chapter 3: Probability Basic Definitions Experiment : A process which leads to a single outcome (called a sample point) that cannot be predicted with certainty. Sample Space (of an experiment): The collection of all the possible outcomes (or sample points). Example 1. Roll 1 die: Sample space = Example 2. Toss 2 coins: Sample space = The probability of a sample point is a number between 0 and 1 that measures the likelihood that this outcome will occur when the experiment is performed. Often we take this to mean the proportion of times the outcome would occur if we repeated the experiment many times. Note: (1) All sample point probabilities must be between 0 and 1. (2) The probabilities of all the points in the sample space must sum to 1.
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Example 1: Probability of rolling a 3, denoted: P(3) = Example 2: Assuming coin is fair, P(HH) = An event is an outcome or collection of outcomes. We typically determine the probability of an event by adding the probabilities of the distinct outcomes that make up the event. Example 1: Event A = ‘rolling an even number’ P(A) = Example 2: Event B = ‘get at least one head’ P(B) = Unions and Intersections Compound events are composed of two or more “simple events,” for example: ± The union of events A and B is the event that either A or B (or both) occurs. ± Denoted A U B ± The intersection of events A and B is the event that both A and B occur when the experiment is conducted. ± Denoted A B
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: Represent graphically which sample points make up which events. Pictures:
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notes515fall10chap3 - STAT 515 - Chapter 3: Probability...

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