prob abd stars

$\in$ (Element of)

Indicates that an object is a member or element of a given set.

Set

A well-defined collection of distinct objects.

A$\subset$ B(Subset)

States that every element of set A is also contained within set B.

A$\cup$ B(Union)

The set containing all elements that belong to A, B, or both.

A$\cap$ B(intersection)

The set containing only the elements that belong to both A and B simultaneously.

A compliant

The set of all elements in the universal set that do not belong to A.

A=B(set equality )

Indicates that sets A and B contain exactly the same elements.

n!(Factorial)

The product of all positive integers less than or equal to n (with 0! = 1)

(n/k)(Binomial coefficient):

The number of ways to choose k elements from a set of n elements,

Random experiment

A procedure or process with a well-defined set of possible outcomes whose specific result is uncertain.

Sample space

The set of all possible outcomes of a random experiment.

Event

A subset of the sample space representing a specific outcome or collection of outcomes.

Event space

A collection of allowable events (subsets of the sample space) to which probabilities can be assigned

$\phi$ (Empty set)

The unique set containing no elements.

A Probability

A function mapping an event to a real number between 0 and 1, representing its likelihood of occurrence

Probability space

A mathematical model consisting of a sample space ($\Omega$ ), an event space (F),and a probability measure (P).

Geometric series:

An infinite sum of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero common ratio (r).