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Statistics_4_3 - Chapter 4 Probability and counting rules...

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Chapter 4: Probability and counting rules 4-1 Sample Spaces and Probability 4–2 The Addition Rules for Probability 4–3 The Multiplication Rules and Conditional Probability 4–4 Counting Rules 4–5 Probability and Counting Rules
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Sample Spaces and Probability A probability experiment is a chance process that leads to well-defined results called outcomes. An outcome is the result of a single trial of a probability experiment. A sample space, S, is the set of all possible outcomes of a probability experiment. Examples: .
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Example : Find the sample space for rolling two dice. Solution: Example : Find the sample space for drawing one card from an ordinary deck of cards. Solution: .
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Example : Find the sample space for the gender of the children if a family has three children. Solution : BBB BBG BGB GBB GGG GGB GBG BGG A tree diagram is a device consisting of line segments emanating from a starting point and also from the outcome point. It is used to determine all possible outcomes of a probability experiment . Example, .
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An event consists of a set of outcomes of a probability experiment . An event with one outcome is called a simple event . a compound event consists of two or more outcomes or simple events. There are three basic interpretations of probability: Classical Probability Classical probability assumes that all outcomes in the sample space are equally likely to occur. Equally likely events are events that have the same probability of occurring. .
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Example: Find the probability of getting a red ace when a card is drawn at random from an ordinary deck of cards. Solution: P (red ace)= g2870 g2873g2870 . Example: A card is drawn from an ordinary deck. Find these probabilities. a. Of getting a jack b. Of getting the 6 of clubs (i.e., a 6 and a club) c. Of getting a 3 or a diamond d. Of getting a 3 or a 6. Solution: a. P(jack)= g2872 g2873g2870 = g2869 g2869g2871 b. P (6 of clubs)= g2869 g2873g2870 c. P (3 or diamond)= g2869g2874 g2873g2870 = g2872 g2869g2871 d. P (3 or 6)= g2876 g2873g2870 = g2870 g2869g2871
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Basic probability rules Probability Rule 1 The probability of any event E is a number between and including 0 and 1. This is denoted by 0 ≤ P ( E ) ≤ 1. Probability Rule 2 If an event E cannot occur (i.e., the event contains no members in the sample space), impossible event, Ø, its probability is 0. Probability Rule 3 If an event E is certain, E=S , then the probability of E is 1 or P(S)=1 . Probability Rule 4 The sum of the probabilities of all the outcomes in the sample space is 1.
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The complement of an event E is the set of outcomes in the sample space that are not included in the outcomes of event E. The complement of E is denoted by g1831 g3364 g1867g1870g1831 g3004 Example : Find the complement of the event E= Rolling a die and getting a 4 or 6. Solution: g1831 g3364 = {1,2,3,5) Complementary Events Rule: Example: If the probability that a person lives in an industrialized country of the world is g2869 g2873 , find the probability that a person does not live in an industrialized country.
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