The idea of conditional probability is used in statistics.
The notion of conditional probability is used in the field of statistics . The expression refers to the existing probability that an event A will occur, knowing that another event B also occurs .
It is important to note that there does not need to be a temporal or causal relationship between A and B. This means that A can occur before B , after or at the same time , and that A can be the origin or consequence of B or not have a causal link.
We must emphasize that in the field of probability there is no space for the concepts of temporal relations or causal relations , although they can play a certain role depending on the interpretation that the observer gives to the events.
The conditional probability is calculated starting from two events or events ( A and B ) in a probabilistic space, indicating the probability that A occurs given that B has occurred. It is written P (A/B) , reading as “probability of A given B” .
Conditional Probability Example
Let's see an example . In a group of 100 students , 35 young people play soccer and basketball , while 80 of the members play soccer . What is the probability that one of the students who plays soccer also plays basketball ?
How likely is it that a student plays football and basketball?
As can be seen, in this case we know two pieces of information: the students who play soccer and basketball ( 35 ) and the students who play soccer ( 80 ).
Event A: A student plays basketball ( x )
Event B: A student plays 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 plays basketball given that he also plays football is 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 to condition , and places greater emphasis on the fact that the probability is not so "free" or "spontaneous", but is subject to a condition. .
We must take a parenthesis to review the concept of probability on its own, 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 the statement is that an event may take place.
Probability is usually expressed in numbers, either in a range from 0 to 1 or from 0 to 100: in both cases, zero indicates that there is no probability of the event taking 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 possibility , although they have clear differences: probability arises from an objective analysis while possibility borders on supposition. In a singing contest, if Carla is clearly more talented than Pedro, she is more likely to win; However, there is a chance that either of them will win because there are many more factors at play than the talent of each one.
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 18th century English mathematician. Basically, it establishes a link between the probability of one direction with the opposite, that is, of "A given B" with "B given A."