In probability theory, a sample space is the set of all possible outcomes of a random experiment. For example, if we roll a six-sided die, the sample space is 1, 2, 3, 4, 5, 6. This means that any time we roll the die, the outcome will be one of these six values.
An event is a subset of the sample space that we are interested in studying. For example, if we are only interested in the outcomes that are greater than 3, the event we are studying is 4, 5, 6. We can also study more complex events that require multiple conditions to be met, such as rolling two dice and looking for the sum to be greater than 9.
An outcome, also called a sample point, is a particular result of the random experiment. For example, if we roll the die and it comes up showing 3, the outcome is 3. It is important to note that an outcome must be a member of the sample space, otherwise it is not a valid outcome.
In summary, sample space is the set of all possible outcomes, event is a subset of the sample space that we are interested in studying, and an outcome is a particular result of the random experiment. These three concepts are the foundation of probability theory and are used to define mathematical models of uncertainty and make quantitative predictions in trading and investment.