Probability Basics

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.

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

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.

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) ​ .

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

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).

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

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.

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

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.