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.


The idea of ​​conditional probability is used in statistics.

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?

Basketball game

How likely is a student to play soccer and 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) = 35/80
P (A / B) = 0.4375
P (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”.