Basics of Probability of Single Events

Probability is a measure of how likely something is to happen.

We may intuitively know that the probability of getting a tail from a fair coin toss is \(50\%\) or \(\frac{1}{2}\) but how do we calculate it?

For a finite sample space with \(n>0\) equally likely outcomes, if \(k\) outcomes satisfy event \(A\), then:

\({\mathrm{P}}(A) = \frac{k}{n} = \frac{\mathrm{Number\ of\ outcomes\ satisfying\ event\ } A}{\mathrm{Total\ number\ of\ possible\ outcomes}}\)

For any event \(A\), \(0\le \mathrm{P}\left( A \right)\le 1\) or \(0\%\le \mathrm{P}\left( A \right)\le 100\%\).

In this finite equally likely model, \(\mathrm{P}\left( A \right)=0\) if and only if event \(A\) is an impossible event.

In this finite equally likely model, \(\mathrm{P}\left( A \right)=1\) if and only if event \(A\) is a certain event.