Question

What is the meaning of conditional probability?

Answer 1

Conditional probability is the probability of a given event assuming that you know the outcome of another event.

If two events are independent, the conditional probability of one event given the other is simply equal to the overall probability of that event. The probability of A given B is written as `P(A|B)`.

Take for example two dependent variables. Define A as being "A random American president's first name is George" and B to be "A random American president's last name is Bush."

Overall, there have been 44 presidents, of which 3 have been named George. 2 of the 44 have been named Bush.

So, `P(A) = 3/44` and `P(B)=2/44`. However, `P(A|B) = 2/2`, because of those 2 presidents named Bush, 2 have been named George.