22_Probability - Other events have probabilities between 0...

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Probability 11/8/11
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Event : a subset of the sample space Ω , satisfying certain axioms.
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Example 5 . A system consists of two subsystems: one with four components and the other with three components. We are interested in only working components of the system. Components fail randomly. The event space and events on the working condition of the system can be formulated as follows.
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Probability measure A probability measure assigns a numerical value in [0, 1] for the probability or chance that an event occurs. A probability of 0 => the event never occurs => an impossible event A probability of 1 => the event always occurs => a certain event
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Unformatted text preview: Other events have probabilities between 0 and 1. Classical probability-- Ω is finite-- all outcomes are equally likely Formal definition of probability measure Axioms of probability measure Example 7 [Rosen, Section 7.1] A bin contains 50 balls labeled 1, 2, . .., 50. What is the probability that balls labeled 11, 4, 17, 39 and 23 are drawn in five consecutive random draws if (a) balls are replaced (put back in the bin) after each draw? (b) balls are not replaced after they are drawn? Theorems Example 5, Section 7.1...
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