The notion of **conditional probability** It is used in the field of **statistics**. The expression refers to the **existing probability that an event A occurs, knowing that another event B also occurs**.

It is important to note that there is no need for a **temporal or causal relationship** Come in **TO** and **B**. This means that **TO** can occur before **B**, after or at the same **weather**, So what **TO** may be the origin or the consequence of **B** or not having a causal link.

We must emphasize that in the field of probability there is no space for the concepts of *temporary relationships* or *causal relationships*, although they can play a certain role according to the interpretation that the **observer** give them to the events.

The conditional probability is calculated starting from two **events** or events (**TO** and **B**) in a probabilistic space, indicating the probability of the occurrence **TO** since it has happened **B**. Is written **P (A / B)**, reading as **“Probability of A given B”**.

## Example of conditional probability

Let’s see a **example**. In a group of **100 students**, **35** youths **they play soccer and basketball**, while **80** of the members practice **soccer**. What is the probability that one of the students who plays **soccer**, also play **basketball** or **basketball**?

As you can see, in this case we know two pieces of information: the students who play **soccer** and to **basketball** (**35**) and students who play **soccer** (**80**).

*Event A:* Have a student play basketball (*x*)*Event B:* Have a student play soccer (*80*)*Event A and B:* Have a student play soccer and basketball (*35*)

*P (A / B) = P (A∩B) / P (B)P (A / B) = 35/80P (A / B) = 0.4375P (A / B) = 43.75%*

Therefore, this **conditional probability** indicates that the probability that a student will play **basketball** since he also plays soccer he is from **43.75%**.

## Conditional probability, another name

Another name by which this concept is known is **conditional probability**. In this case another adjective is used, which in turn is the participle of the verb *condition*, and places greater emphasis on **done** that probability is not so “free” or “spontaneous”, but is subject to a condition.

We must make a parenthesis to review the concept of **probability** by itself, since we use it quite frequently in everyday speech, although in the scientific field it has a much stricter definition. In short, it is a **measure** that allows us to estimate how true is the statement that an event can take place.

In general, the probability is expressed in numbers, either in a **rank** that goes from 0 to 1 or from 0 to 100: in both cases, zero indicates that there is no probability that the event will take place, while one and one hundred indicate with certainty that it can take place.

## Difference between probability and possibility

This concept is often confused with that of *possibility*, although they have clear differences: the probability arises from a **analysis** objective while possibility borders on assumption. In a singing contest, if Carla is clearly more talented than Pedro, she has a better chance of winning; however, there is a chance that either of them will win because there are many more factors at play than the talent of each.

Returning to conditional probability, if we are studying a random event in which A can occur if B occurs, it is possible to apply the so-called **Bayes theorem**, proposed by **Thomas bayes**, an English mathematician of the 18th century. Basically, it raises a link between the probability of a **sense** with the opposite, that is to say “A given B” with “B given A”.