Please study the figure given below:PeroK said:
A probability space is a mathematical concept used to model random events or experiments. It consists of three components: a sample space, an event space, and a probability function.
A sample space is a set that contains all possible outcomes of an experiment. It is usually denoted by the symbol Ω and can be finite, countably infinite, or uncountably infinite.
An event space is a collection of subsets of the sample space that represent different events or outcomes of an experiment. It is denoted by the symbol ℱ and can contain singletons, unions, intersections, and complements of events.
Probability is a numerical measure of the likelihood of an event occurring in a probability space. It is defined as a function P that maps events to real numbers between 0 and 1, where 0 represents impossibility and 1 represents certainty.
Probability spaces are used in various fields such as statistics, finance, physics, and engineering to model and analyze random phenomena. Some examples include predicting stock market trends, designing reliable computer networks, and understanding the behavior of subatomic particles.