Probability is the branch of mathematics that deals with the analysis of random phenomena. The randomness in Probability comes from the fact that we cannot predict the outcome of a certain event with absolute certainty. Probability theory is used to quantify the degree of uncertainty and to make predictions about the likelihood of certain events occurring.
The basis for Probability theory is set theory, which is the study of sets and their relationships. In Probability, a set is a collection of elements (e.g., people, objects, events) that have something in common. The relationship between two sets is called a function. A function assigns a unique element from one set to every element in another set. For example, if we have a set A consisting of the numbers 1, 2, 3, 4, and 5, and we have a set B consisting of the letters A, B, C, D ,and E , then we can define a function f such that f(1)=A ,f(2)=B ,f(3)=C ,f(4)=D ,and f(5)=E . This function would be called a one-to-one correspondence between sets A and B .
In order to use Probability theory to analyze random phenomena, we need to first understand what kind of events we are dealing with. There are two types of events: those that are mutually exclusive and those that are not mutually exclusive . Mutually exclusive events are those where only one event can occur at any given time (e.g., flipping a coin and getting either heads or tails). Non-mutually exclusive events are those where more than one event can occur at any given time (e..g