Chapter 1 Probability (review)

This chapter is a revision of essential basics from the Year 1 module on probability.

Probability is a measure of the chance that an event may occur, in the same way that length is a measure of the magnitude of an object. In particular, probability is defined on the framework of events. This framework consists of:

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  the (elementary) outcomes of an experiment, $\omega$;

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  the sample space $\mathrm{\Omega }$ is the list (possibly infinite or uncountable) of all these outcomes;

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  the events, which are subsets of the sample space.

The set of outcomes in the sample space have the properties of being exhaustive (all possible outcomes are listed), and exclusive (no two outcomes can both occur).

E.g. flip a coin twice.

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  The outcomes are HH,HT,TH and TT

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  $\mathrm{\Omega }=\{HH,HT,TH,TT\}$

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  the events include $\{HT\}\cup \{TH\}$, $\{TT\}$, $\varphi$, and $\mathrm{\Omega }$.