The likelihood of something happening, defined as a number between 0 and 1 If something will never happen, it has a probability of 0; if it is certain to happen, it has a probability of 1.
- Experiment: observation of some activity or the act of taking some measurement.
- Outcome: result of an experiment
- Sample space: The set of all possible outcomes. Also known as Sample space. The notation is omega(Ω).
- Partition: set of mutually exclusive events, part of the Sample space.
- Probability mass: The sample space has a probability mass of 1.
- Uniform distribution: every event has the same likelihood of occurring.
Collection of one or more outcomes of an experiment is known as an event. It is also described as a subset of the Sample space. The notation is Greek letter sigma (Σ).
Events can be impossible, certain or something in between.
Two or more events can be:
- mutually exclusive or disjoint: P (A ∩ B) = 0. The "∩" symbol means: union, is referred to as "cap" and may be read as "and".
- joint. The probability of A OR B occurring: P (A ∪ B). The "∪" symbol means: not the union, is referred to as "cup" and may be read as "or".
- independent : X ⊥ W
- conditional: P (A | B). The “|” symbol means “given that”. In the table below it is written as "┃" for technical reasons.
- complement: P (A') or (¬ A)
- random variables written as upper case: X, Y,
- expected value: E[X]
|Mutually exclusive or disjoint||The probability of A occurring or the probability of B occurring||Special Rule of Addition||P(A or B) = P(A)+ P(B)||P(A + B) = P(A)+ P(B)||P(A ∪ B) = P(A) + P(B)||P(A ∩ B) = 0|
|Joint||The probability that either A may occur or B may occur followed by the possibility that both A and B may occur||General Rule of Addition||P (A or B) = P(A)+ P(B) – P(AB)||P (A or B) = P(A)+ P(B) – P(A and B)||P(A ∪ B) = P(A) + P(B) - P (A ∩ B)|
|Independent||The probability that A and B will occur||Special Rule of Multiplication||P(A and B) = P(A)P(B)||P (A ∩ B) = P(A) P(B)||P(A1A2...An)=P(A1)P(A2)...P(An)|
|Conditional||P(B┃A) – probability that event B will occur given that event A has already occurred||General Rule of Multiplication||P(A and B) = P(A)P(B┃A) = P(B) P(A┃B)||P(A ∩ B) = P(A) P(B┃A) = P(B) P(A┃B)|
|Complement||Event Not occurring – or Neither/nor will happen||Complement Rule||P(A) = 1 – P (¬ A)|
|Probability Mass Function||Probability Density Function|