# Definition:Conditional Probability

Jump to navigation
Jump to search

## Definition

Let $\EE$ be an experiment with probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $A, B \in \Sigma$ be events of $\EE$.

We write the **conditional probability of $A$ given $B$** as $\condprob A B$, and define it as:

*the probability that $A$ has occurred, given that $B$ has occurred.*

## Also see

- Chain Rule for Probability, where it is shown that $\condprob A B = \dfrac {\map \Pr {A \cap B} } {\map \Pr B}$.

- Results about
**conditional probabilities**can be found here.

## Technical Note

The $\LaTeX$ code for \(\condprob {A} {B}\) is `\condprob {A} {B}`

.

When the arguments are single characters, it is usual to omit the braces:

`\condprob n p`

## Sources

- 1988: Dominic Welsh:
*Codes and Cryptography*... (previous) ... (next): Notation - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**conditional probability**

This page may be the result of a refactoring operation.As such, the following source works, along with any process flow, will need to be reviewed. When this has been completed, the citation of that source work (if it is appropriate that it stay on this page) is to be placed above this message, into the usual chronological ordering.In particular: See whether Chain Rule for Probability is given hereIf you have access to any of these works, then you are invited to review this list, and make any necessary corrections.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{SourceReview}}` from the code. |

- 1986: Geoffrey Grimmett and Dominic Welsh:
*Probability: An Introduction*... (previous) ... (next): $1$: Events and probabilities: $1.6$: Conditional probabilities: $(19)$