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Unformatted text preview: Chapter 18 Probability Models Outline Probability Models Outcomes & Events Probability Rules Probability Models for Sampling Probability Models Definition A probability model for a random phenomenon describes the possible outcomes of the phenomenon and assigns probabilities to any collection of those outcomes. An outcome for an experiment is a possible result of an experiment. A collection of outcomes is called an event . Each individual outcome is also an event. Example Suppose we flip two coins. There are 4 possible outcomes if we keep track of the separate tosses. What are they? Suppose that we only count the number of heads. What are the possible events ? Why is the event 1 head not an outcome? Is the event 0 heads an outcome & an event? Assigning Probabilities To Events There are two ways (not counting personal probabilities) to assign probabilities to events. 1. Mathematical argument Make reasonable assumptions and use them to argue probabilities for events. 2. Use data Repeat an experiment/phenomenon many times and count the number of times out of the total that the event occurred. Both involve considering the proportion of times that an event should occur in the long run. Mathematical Argument Example: Flip two coins and consider the number of heads. What are the probabilities? EVENTS: 0 heads 1 head 2 heads Probability: How did we assign the probabilities? It turns out we used some probability rules without knowing it. Later on . . . Using Data Marital status of all women aged 24 to 29. Marital Status: Never Married Married Widowed Divorced Probability: .404 .535 .004 .057 The proportion of all women aged 24 to 29 who have never been married is .404. We use this proportion as a probability. Why might you say this probability assigning method is approximate? What is the probability that a randomly selected woman is widowed? What about the event married or divorced? Probability Rules 4 Probability Rules 1. Any probability must be between 0 and 1. 2. The event of all possible outcomes together have probability 1 of occurring. 3. If two events have no outcomes in common, then the probability of either of their events occurring is the sum of each events probability. 4. The probability that an event does not occur is 1 minus the probability that an event does occur. A Closer Look 1. A probability must be between 0 and 1....
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 Fall '07
 JOHNSON
 Probability

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