(Text as at 12/08/2007 10:17:46)

**Ideally, we would like to assign a mathematical probability to any statement, ie. a real number in the range 0 to 1, with 0 representing impossibility & 1 representing certainty. As in the frequency theory of probability, the assigned number should represent the proportion of situations in which the statement is expected to turn out to be true.**

- However, in most cases this approach has a spurious aura of precision, because most situations are not regular or repeatable events.
- It must be noted that where the possible outcomes of an experiment form a continuum or other infinite set, the a priori probability of any particular outcome is 0. Nonetheless, we would not describe any particular outcome, a posteriori, as unlikely. Rather, we would divide the domain of possible outcomes into equivalence classes (whose total probability may be obtained by summation or integration) and judge the outcome of the experiment by the probability of its class.

Note last updated | Reference for this Topic | Parent Topic |
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12/08/2007 10:17:46 | 459 (Probability - Issues) | Probability |

Probability |

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Todman (Theo) | Thesis - Probability | Paper | Yes |

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