BUS152-Ch04 - BUS152 - Statistics for Social Sciences...

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BUS152 - Statistics for Social Sciences Spring 2011 Chapter 4: Basic Probability
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2 Basic Probability Concepts Probability – the chance that an uncertain event will occur (always between 0 and 1) Impossible Event – an event that has no chance of occurring (probability = 0) Certain Event – an event that is sure to occur (probability = 1)
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3 Assessing Probability There are three approaches to assessing the probability of an uncertain event: 1. a priori -- based on prior knowledge of the process 2. empirical probability 3. subjective probability outcomes elementary of number total occur can event the ways of number T X = = based on a combination of an individual’s past experience, personal opinion, and analysis of a particular situation outcomes elementary of number total occur can event the ways of number = Assuming all outcomes are equally likely probability of occurrence probability of occurrence probability of occurrence
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4 Example of a priori probability Find the probability of selecting a face card (Jack, Queen, or King) from a standard deck of 52 cards. cards of number total cards face of number Card Face of y Probabilit = = T X 13 3 cards total 52 cards face 12 = = T X
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5 Example of empirical probability Taking Stats Not Taking Stats Total Male 84 145 229 Female 76 134 210 Total 160 279 439 Find the probability of selecting a male taking statistics from the population described in the following table: 191 . 0 439 84 people of number total stats taking males of number = = = Probability of male taking stats
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6 Events Each possible outcome of a variable is an event . Simple event An event described by a single characteristic e.g., A red card from a deck of cards Joint event An event described by two or more characteristics e.g., An ace that is also red from a deck of cards Complement of an event A (denoted A’) All events that are not part of event A e.g., All cards that are not diamonds
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7 Sample Space The Sample Space is the collection of all possible events e.g. All 6 faces of a die: e.g. All 52 cards of a bridge deck:
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8 Visualizing Events Contingency Tables Decision Trees Red 2 24 26 Black 2 24 26 Total 4 48 52 Ace Not Ace Total Full Deck of 52 Cards R e d C a r B l c k N o t n A t a Sample Space Sample Space 2 24 2 24
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9 Visualizing Events Venn Diagrams Let A = aces Let B = red cards A B A ∩ B = ace and red A U B = ace or red
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10 Definitions: Simple vs. Joint Probability Simple Probability refers to the probability of a simple event. Ex: P(King)
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BUS152-Ch04 - BUS152 - Statistics for Social Sciences...

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