There are three ways to think about probability:

1. The classical definition.
2. Relative-frequency definition.

3. The subjective probability/ personal-probability definition (probability as a measure of belief).

4. Number of ways the event can occur/The total number of outcomes
   Note: All outcomes are “equally likely”.

5. When something happens (or can happen) over and over again, we can apply a relative-frequency interpretation.

Probability of a specific outcome is defined as the proportion of times it occurs over the long run.

1. Subjective Probability, since it is personal, there is no “single correct answer”.

Experiment is any action, phenomenon or process that can be infinitely repeated, at least in theory.

Trial is a single repetition of the experiment.

Sample Space of an experiment denoted by S, is the set of all possible distinct outcomes of that experiment.

The Sample Space of rolling 1 die:

S = {1, 2, 3, 4, 5, 6}

2 dice:

S = {1, 2, 3, 4, 5 … 36}

You can get 36 since \(6^2\). There are two six sided dice.

The sample space may be either discrete or non discrete (continuous). A sample space is discrete if it consists of a finite or countably infinite set of simple events.

S= {a1, a2, a3,…} S= {1, 2, 3, 4,…} All positive integers. S= { 1/2, 1/3, 1/4, 1/5…} All rational numbers. We say a set is discrete if the elements in it are ‘separated’.

A sample space is continuous if it contains an interval (either finite or infinite ) of real numbers.