C1100__15 - Sets Reminder Set S sample space includes all...

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1 Sets: Reminder Set S – sample space - includes all possible outcomes A S (subset of S) = complement of A Intersection (A and B) Union (A or B) A A S A B A A B B A S B A
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2 Probability Rules 1. Any probability is a number between 0 and 1 For any event A, 1. All possible outcomes together must have probability 1: 3. The probability that an event does not occur is 1 minus the probability that the event does occur. p(A c )=1-p(A) 4. The probability that a empty set occurs is zero ( 29 1 S p = 1 p(A) 0 0 ) p( = φ
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3 Assigning probability to equally likely outcomes Example Find the probability of obtaining an even number in one roll of a die Answer: There are 6 equally likely outcomes : 1,2,3,4,5,6 S={1,2,3,4,5,6} A={an even number is observed on the die} = {2,4,6} 5 . 0 6 3 S in outcomes of # A in outcomes of # ) ( = = = A P The probability of an odd number = A c . P(A c )=1-p(A)=0.5
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4 Die example: A={1,3} B={1,4,6} The additive law of probability ) ( ) ( ) ( ) ( B A P B P A P B A P - + = A B S B A 6 4 6 1 6 3 6 2 ) ( = - + = B A P } 6 , 5 , 4 , 3 , 2 , 1 { = S
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Example Let A be the event that a student gets an A in an exam, and let F be the event that a student is female. Suppose p(A)=.25 and p(F)=.40, and p(A F)=.10. Find p(A F). Answer: if we simply add p(A) and p(F) we will be counting the overlap p(A F) twice. Therefore:
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This note was uploaded on 11/03/2009 for the course IST IST taught by Professor N/a during the Spring '09 term at Anadolu University.

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C1100__15 - Sets Reminder Set S sample space includes all...

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