# Probability overview

### Probability

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.