Joint Probability: Definition, Formula & Examples

KEY TAKEAWAYS

• Joint probability is a statistical measure that calculates the probability of two events occurring at the same time. 
• The two events that occur during joint probability have to be independent of each other.
• Joint probability differs from conditional probability. This is on the basis that a conditional probability is a probability that one event will happen given that another event or action happens.

What Is Joint Probability?

Joint probability is a statistical measure. It calculates the probability that two events occur together and at the same point in time. This tends to be put across as the probability that event Y occurs at the same time that event X also occurs. 

The Formula for Joint Probability

The joint probability formula can be portrayed in slightly different ways. The joint distribution formula which represents the probability of events intersecting each other is as follows: 

How to Calculate Joint Probability

Let’s use the example above again. 

There are two black Jacks in a card deck. The Jack of Spades and the Jack of Clubs. That would mean the formula is as follows:

P(J⋂ Black) = 2/52 = 1/26

The two events “Jack” and “Black” are independent of each other. This means you could also use the following formula in order to calculate the joint probability. 

P(J∩Black) = P(Jack) × P(Black) = 4/52 × 26/52 = 1/26

The “⋂” symbol is referred to as the intersection. So the probability of event X and event Y happening is the same as the point where the two events intersect.

Joint Probability Example

Joint probability deals with the likeliness of something happening. It can be quantified by a number that is between 0 and 1. Where 0 is when an event is impossible and will not occur, and 1 is a certain, 100% chance that the event will occur.

So for example, if you flip a coin, there is a 50-50 probability it will be tails, or 0.5. This means that there is an equal probability that it will be heads or tails. 

Or let’s say that you’re picking a card from a deck of cards. There are 26 red cards and 26 black cards. Joint probability will come into play when you figure out the possibility of picking both a black card, and a Jack. 

Joint Probability vs Conditional Probability

The joint probability theory is not the same as conditional probability, though the two are often confused. 

Conditional probability can be defined as the probability that one event will happen given that another event or action happens. This can be formulaically shown as follows: 

P (X, given Y) or P(X\Y)

This essentially means that the chance of one event happening is conditional. The condition being that another event happens.

Summary

Joint probability is a statistical measure that can be used to calculate the likelihood of two events occurring simultaneously. For joint probability calculations to work accurately, they must be independent events. 

In the financial sector, a joint probability function is a useful tool for potential investors. As well as business owners that are concerned with statistical measures. 

Statisticians and analysts can use the joint probability function to try and predict when two events will occur simultaneously. The data brought forward from this can help to predict things like share prices.