DefinitionsΒΆ
Any experiment with randomness can produce one outcome of the many possible, denoted by the lowercase Greek letter Omega \(\omega\). The outcome space, denoted by the uppercase Greek letter Omega \(\Omega\), is the set, or collection of all possible outcomes.
A single event is a subset of \(\Omega\), commonly denoted by increasing order of uppercase alphabets, starting with \(A\), \(B\), etc. The empty set and the entire set \(\Omega\) are both valid subsets.
Note that an outcome \(\omega_1\) is different than the event \(A=\{\omega_1\}\), where the former is a single outcome, but the latter is a set with a single element.
\(P(A)\) is the probability that \(A\) will occur.
If all \(n\) outcomes in \(\Omega\) are equally likely, then \(P(A)\) is denoted by \(\text{number of outcomes where A occurs}/\text{number of outcomes in }\Omega\).