# Ch2etman - PROBABILITY CHAPTER 2 AXIOMS OF PROBABILITY...

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Theory of Probability / Prof.Dr.M.Nahit Serarslan PROBABILITY CHAPTER 2 AXIOMS OF PROBABILITY

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Theory of Probability / Prof.Dr.M.Nahit Serarslan Contents Sample Space and Events Definition of Sample Space Definition of Event Union of Events Intersection of Events Null Event Mutually Exclusive Events DeMorgan’s Laws Axioms of Probability Some Simple Propositions Sample Spaces Having Equally Likely Outcomes Probability as a Continuous Set Function
Theory of Probability / Prof.Dr.M.Nahit Serarslan Sample Space: All possible outcomes of an experiment is known as the sample space of the experiment and is denoted by S .

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Theory of Probability / Prof.Dr.M.Nahit Serarslan Examples: 1. If the outcome of an experiment consists of the gender of a new born child, then: 2. If the experiment consists of flipping two coins, then the sample space will be the following four points: { } b g S , = { } ) , ( ), , ( ), , ( ), , ( T T H T T H H H S =
Theory of Probability / Prof.Dr.M.Nahit Serarslan Examples: 3. If the experiment consists of measuring (in hours) the life time of a transistor, then: 4. If the outcome of an experiment is the order of finish in a race among 7 horses having post positions 1, 2, 3, 4, 5, 6, 7 then S= { all 7! permutations of (1, 2, 3, 4, 5, 6, 7)} where the outcome (2,3,1,6,5,4,7) means, for instance, that the number 2 horse comes in first, then number 3 horse, then number 1 horse, and so on. { } < = x x S 0 :

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Theory of Probability / Prof.Dr.M.Nahit Serarslan Event: Any subset E of the sample space is known as an event . If the outcome of the experiment is contained in E, then we say that E has occurred.
Theory of Probability / Prof.Dr.M.Nahit Serarslan Examples: 1. In the gender of a child example above, if we take E as the event that the child is a girl, then, 2. S : Flipping two coins E : A head appears on the first coin { } b g S , = { } g E = { } ) , ( ), , ( ), , ( ), , ( T T H T T H H H S = { } ) , ( ), , ( T H H H E =

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Theory of Probability / Prof.Dr.M.Nahit Serarslan Examples: 3. S : Lifetime of a transistor (in hours) E : Transistor does not last longer than 5 hours 4. S : Order of finish in a race among 7 horses S = { all 7! permutations of (1, 2, 3, 4, 5, 6, 7) } E : Horse 3 wins the race E = {all outcomes of S starting with a 3} { } = x x S 0 : { } 5 0 : = x x E
Theory of Probability / Prof.Dr.M.Nahit Serarslan Definition 1: Let E and F be two events of a sample space S. The event E F is called the union of the events E and F . This consists of all points that are either in E or in F or both in E and F .

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Theory of Probability / Prof.Dr.M.Nahit Serarslan Definition 2: The event EF is called the intersection of E and F . This consists of all outcomes that are both in E and F and can also be written as E F .
Serarslan Definition 3: If the event EF doesn’t contain any outcomes, we shall refer to it as the

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## This note was uploaded on 11/27/2010 for the course ENGINEERIN 23 taught by Professor Nahiterarslan during the Spring '10 term at Istanbul Technical University.

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Ch2etman - PROBABILITY CHAPTER 2 AXIOMS OF PROBABILITY...

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