Conditional probability 

In a nutshell

In probability, sometimes events may be dependent on each other, especially when there are sequential events (one events occurs after another event). If the probability of the second event changes depending on whether the first event has occurred or not, then conditional probability can be used.

Calculating conditional probabilities

Conditional probabilities can be calculated using a sample space diagram, a Venn diagram or a tree diagram. The idea is to calculate the probability of an event occurring from a subset of the sample where a previous event has occurred. 

Procedure

Example

In a class of $$30$$ students, $$20$$ are brunette and, of those $$20$$, $$18$$ are brown eyed.

If a student is chosen at random, what is the probability of him being brown eyed (A), given that he's brunette (B)?

You can solve the problem using a two-way table:

There are $$20$$ students who are brunette, of which there are $$18$$ students who are brown eyed.

$$P(A|B)=\dfrac{18}{20}=\dfrac{9}{10}$$​​