Probability overview


The extent to which an event is likely to occur. Probability is measured on a 0-1 scale where 1 is an absolute 100% certainty and 0 is an impossible event.


P(A) = n(E)/n(S) where n(E) is the number of events of interest and n(S) is the total number of possible events in the sample.



Joint probability

The probability that two events occur together. These probabilities can be measured with a multiplication rule:
P(A and B) = P(A) x P(B)


To calculate the probabilities of two mutually exclusive events, you would require an addition rule:
P(A or B) = P(A) + P(B)



Conditional probability

Where the probability of an event depends on the probability of another event beforehand. These can be measured by this formula:
P(A and B) = P(A) x P(B|A) where P(B|A) is the probability that B occurs, given A.



Independent vs Dependent events

In an independent event, the probability is not affected by any previous events. E.g. rolling a dice. When the probability of an event is influenced by prior events this is known as a dependent event. E.g. the probability of choosing a face card from a deck of cards changes based on the cards already chosen.



Mutually inclusive vs mutually exclusive events

Mutually exclusive events cannot occur at the same time e.g. a number can be either odd or even, never both. Mutually inclusive events can occur at the same time. For example a number can be both even and less than 10. The probability calculation therefore needs to take into account both possibilities. Venn diagrams are useful visuals to express this.



Confidence interval

A calculation which provides a percentage confidence of the probability of a parameter falling within particular values, based on known values for related variables.


For example your z-test could return a confidence interval on a survey question where respondents have scored 1-10 which may state 95% confidence that customer satisfaction is between 7 and 8 out of 10.