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Probability space
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==== Example 1 ==== If the experiment consists of just one flip of a [[fair coin]], then the outcome is either heads or tails: <math>\Omega = \{\text{H}, \text{T}\}</math>. The Ο-algebra <math>\mathcal{F} = 2^{\Omega}</math> contains <math>2^2 = 4</math> events, namely: <math>\{\text{H}\}</math> ("heads"), <math>\{\text{T}\}</math> ("tails"), <math>\{\}</math> ("neither heads nor tails"), and <math>\{\text{H}, \text{T}\}</math> ("either heads or tails"); in other words, <math>\mathcal{F} = \{\{\}, \{\text{H}\}, \{\text{T}\}, \{\text{H}, \text{T}\}\}</math>. There is a fifty percent chance of tossing heads and fifty percent for tails, so the probability measure in this example is <math>P(\{\}) = 0</math>, <math>P(\{\text{H}\}) = 0.5</math>, <math>P(\{\text{T}\}) = 0.5</math>, <math>P(\{\text{H}, \text{T}\}) = 1</math>.
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