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.