Probability of events

Summary

The notation \(P(A)\)

• If \(A\) is an event , then \(P(A)\) denotes the probability of that event (the probability that the event will happen or be true).

Example

• \(S={1,2,3,4,5,6}\) and \(A={1,2,3}\) is an event. Then \(P(A)=P({1,2,3})\) denotes the probability that the experiment will result in the outcome 1,2 or 3 and not in 4,5 or 6.

Equally likely

• If our sample space contains a finite number of possible outcomes and each outcome is equally likely then we can calculate the probability of every possible event.

Example

• We toss a symmetric dice (not loaded or shaved) and the toss is fair (does not favor any particular outcome) and assume that each outcome is equally likely. With \(S={1,2,3,4,5,6}\) and \(A={1,2,3}\) we then have \(P(A)=3/6=1/2\) or a 50% chance of tossing 1,2 or 3.
• In general, if \(S\) contains \(n\) elements and an event \(A\) contains \(k\) elements then \(P(A)=k/n\) if each outcome is equally likely.