## 3.3 The Probability Measure

To create a mathematical model which will enable us to quantify the likelihood of the various outcomes of the experiment, we attach to each event a number between 0 and 1 which will be called the probability of the event. It can be thought of as the relative frequency of occurrence of the event in a large number of repetitions of the experiment. The probability of event A will be denoted by P( A). The probability measure satisfies the following axioms:

1. 0 ? P( A) ? 1 for all P( A).

2. P( S) = 1 and P( ) = 0.

3. If A ? B = (i.e. A and B are mutually exclusive), then P( A ? B) = P( A) + P( B).

It follows immediately from the axioms that if { A 1, A 2, , A n} is a partition then

Examples

1. Consider a room of fire origin with one door and one window. There are four possible situations, namely: door and window closed, door and window open, door open and window closed, and door closed and window open. By analysing observations on actual fires, we may come to the conclusion that the relative frequencies of these four events are 0.1, 0.2, 0.4 and 0.3.

2. Returning to the maximum temperature T in...

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##### Topics of Interest

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Notes 1.4: Axioms and properties of probability Note 1. When the sample space ? is finite or countably infinite, P( A) is usually defined for all subsets of ? by taking for some nonnegative function...

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