Conditional probability - Rules of Probability

This is the probability associated with combinations of events but given that some prior result has already been achieved with one of them.

It's expressed in the form of

P(x|y) = Probability of x given that y has already occurred.

P(x|y) =  P(xy)/P(y) → conditional probability formula.

Illustration

In a competitive examination 30 candidates are to be chosen.  In all 600 candidates appear in a written test, and 100 will be call for the interview.

(i) What is the probability that a person will be called for the interview?

(ii) Find out the probability of a person getting chosen if he has been called for the interview?

(iii) Probability that person is called for the interview and is chosen?

Solution:

Assume event A be that the person is called for the interview and event B that he is chosen.

(i) P(A) = 100/600  = 1/6 

(ii) P(B|A) =  30/100 = 3/10

(iii) P(AB) = P(A) × P(B|A)

=  (1/6) * (3/10) = 3/60 = 1/20