# Joint Probability

Written By:
Paul Tracy
Updated August 5, 2020

## What is Joint Probability?

Joint probability is the likelihood of more than one event occurring at the same time.

## How Does Joint Probability Work?

he joint probability for two events, A and B, is expressed mathematically as P(A,B). Joint probability is calculated by multiplying the probability of event A, expressed as P(A), by the probability of event B, expressed as P(B).
For example, suppose a statistician wishes to know the probability that the number five will occur twice when two dice are rolled at the same time. Since each die has six possible outcomes, the probability of a five occurring on each die is 1/6 or 0.1666.

P(A)=0.1666
P(B)=0.1666

P(A,B)=0.1666 x 0.1666)=0.02777

This means the joint probability that a five will be rolled on both dice at the same time is 0.02777.

## Why Does Joint Probability Matter?

Joint probability is a useful statistic for analysts and statisticians to use when two or more observable phenomena can occur simultaneously (for example, a decline in the Dow Jones Industrial Average accompanied by a substantial loss in the value of the dollar). It indicates the likelihood two separate events will occur simultaneously.
However, it is important to know that joint probability cannot be used to determine how much the occurrence of one event influences the occurrence of another event. For this, one would need to calculate a conditional probability.