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Sample Space and Events

Before you can compute a probability you have to say precisely what might happen. This sounds like bookkeeping. It is actually where most wrong answers come from.

The sample space Ω\Omega is the set of all possible outcomes. For one roll of a six-sided die:

A sample space
Ω={1,2,3,4,5,6}\Omega = \{1, 2, 3, 4, 5, 6\}

Every outcome the experiment can produce, listed once. An event is any subset of it.

An event is any subset of Ω\Omega. Rolling a 3 is the simple event {3}\{3\}; rolling an even number is the compound event {2,4,6}\{2, 4, 6\}.

The choice of sample space is a modelling decision

Consider flipping two coins. Write the sample space as the set of possible head counts:

Ω1={0 heads,1 head,2 heads}\Omega_1 = \{0 \text{ heads}, 1 \text{ head}, 2 \text{ heads}\}

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