The notion of conditional probability It is used in the field of statistics . The expression refers to the existing probability of an event A happening, knowing that another event B also occurs .
It is important to keep in mind that there is no need for a temporal or causal relationship between TO and B . This means that TO may occur before B after or at the same weather , and that TO it can be the origin or the consequence of B or not have a causality link.
Conditional probability is calculated from two events or events (TO and B ) in a probabilistic space, indicating the probability of its occurrence TO since it has happened B . Is written P (A / B) , reading as "Probability of A given B" .
Let's see a example . In a group of 100 students , 35 young boys they play soccer and basketball , while 80 of the members practice soccer . What is the probability that one of the students who plays at soccer , also play basketball or basketball ?
As you can see, in this case we know two facts: the students who play soccer and at basketball (35 ) and the students who play soccer (80 ).
Event A: For a student to play basketball (x)
Event B: For a student to play football (80)
Event A and B: For a student to play football 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 of a student playing at basketball since he also plays football is 43,75% .