Probability Basics

Probability is a measure of the likelihood that a particular event will occur, typically expressed as a fraction, decimal, or percentage between 0 and 1.

P(A)= Total number of possible outcomes/ Number of favorable outcomes ​ .

A probability of 0 means the event is impossible and will not happen. A probability of 1 means the event is certain and will definitely happen.

A random experiment is a process that leads to one of several possible outcomes, with the outcome not being predictable in advance.

For mutually exclusive events, P(A or B)=P(A)+P(B). For non-mutually exclusive events, P(A or B)=P(A)+P(B)−P(A and B). If A and B are independent, P(A and B)=P(A)×P(B).

Conditional probability is the probability of an event occurring given that another event has already occurred, denoted as P(A∣B).

Bayes' Theorem is a formula that calculates the probability of an event based on prior knowledge of conditions related to the event: P(A∣B)= P(B∣A)⋅P(A)/P(B) ​ .

Complementary events are pairs of events where one occurs if and only if the other does not. The probability of an event A plus the probability of its complement P(A)+P(A′)=1.

The expected value is the average outcome of a random variable over many trials, calculated as E(X)=∑[x⋅P(x)].

The Law of Large Numbers states that as the number of trials increases, the experimental probability of an event will get closer to its theoretical probability.