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Unformatted text preview: Probability Probability Theory • Difficult to define probability formally – Every day life gives us of chance/probability • Will the bus be on time? • Will we pass the exam? • Shall we bet on this horse? – Mostly use subjective probability to deal with such questions • Intuition, experience • Experiment – Observing, or measuring some activity • Outcome – A particular result of the experiment • Sample Space – A set of all outcomes of the experiment, denoted by S • Event – Collection of one or more possible outcomes which have some attribute in common Venn Diagram • Used to represent sample spaces and events pictorially – Toss a die – possible outcomes are – O 1 ={1}, O 2 ={2}, O 3 ={3}, O 4 ={4}, O 5 ={5}, O 6 ={6} – Suppose event E =“score greater than 4” = {5,6} – E is represented by pink oval Rectangle represents sample space, S E O 1 . O 2 . O 5 . O 6 . O 3 . O 4 . Classical concept of probability • Suppose that there are n equally likely outcomes of an experiment and an event E which can happen in w ways, then the probability that event E occurs is defined by P(E) where n w E P = ) ( Properties of probability • If an event E cannot occur, P(E) = 0 • If an event E always occurs, P(E) = 1 • If S is the sample space, the collection of all possible outcomes, then P(S) = 1 1 ) ( ≤ ≤ E P n w ≤ ≤ since Venn Diagram • Used to represent sample spaces and events...
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This note was uploaded on 04/07/2012 for the course IBE 340 taught by Professor Valerieozaki during the Spring '09 term at Sophia University.
 Spring '09
 ValerieOzaki

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