Probability means how likely an event can occur and conditional probability is how likely an event can occur given another event has already occurred. There is a dependence between the events.
P(B/A) = P(A,B)/P(A)
P(B/A) – Probability of B given A
P(A,B) – Probability of both B and A
P(A) – Probability of A
For example :- Students given two tests A and B. 60% of students passed both tests and 80% of students passed first test. Let we want to know how likely is it if a student passed first test he will pass second test also.
P(A) = 80/100 = 0.80
P(A,B) = 60/100) = 0.60
We want to find P(B/A) – pass test B given passed test A
P(B/A) = 0.60/0.80 = 0.75
Now we can also understand Bayes’ Theorem.
P(A/B) = P(A) P(B/A) /P(B)
P(A,B) = P(A) P(B/A)