Unformatted text preview: 5 Properties of Probability a The set of all possible outcomes is called the sample space S
0 An event is any collection or subset of the outcomes contained in S i A simple event is exactly one outcome, a compound event consists of more than one
outcome 0 Let .9 be a sample space and let A be an event. Denote the probability of A occurring as P (A)
o Axiom 1: All probabilities are betWeen 0 and l, P(A) E [0, 1} for any A I Axiom 2: The total probability of the sample space is 1, P(.S') = 1, the outcome will
be somewhere in the szunple space a The probability of the empty set is zero, PM) =
a Let A be an event and let AC be the compliment. Then P(AC) : l — PUT). W“ 0 Let A and B be events such that A C B. Then, PM) 3 P(B)_  Example: Consider a system which consists of three components which either pass or
fail a. reliability test. Recall the sample space, Let A be the set of all outcomes Where
the third component passes the reliability test. Let B be the set of all outcomes where
the second component passes the reliability test What is P( )and PW ti PW): '4 :gJ5 oer/ease
Rest9% {Dotti its?) H5):  Let A and B be events. The probability of the union of A and B is given by
P(A U B) = P(A) + 13(3) — P(A F] B)  Example: Consider a system which consists of three components which either pass or
fail a. reliability test. Recall the sample Space. Let A be the set of all outcomes where
the third component passes the reliability test. Let B be the set of all outcomes where
the second component passes the reliability test. What is P(A H B) and P(A U B)? ...
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 Fall '07
 Carlton

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