Question

What is the definition of conditional probability?

Answer 1

The conditional probability of an event B is the probability that the event will occur given the knowledge that an event A has already occurred.

Explanation:

The conditional probability of an event B is the probability that the event will occur given the knowledge that an event A has already occurred. This probability is written `P(B|A)`, notation for the probability of B given A.

In the case where events A and B are independent (where event A has no effect on the probability of event B), the conditional probability of event B given event A is simply the probability of event B, that is `P(B)`.

Example: Suppose there are 2 blue and 3 red marbles are in a bag. What is the probability of getting two blue marbles, say without replacement? Chances of getting first marble appear to be `2/5`, but after taking it out, as the same is not replaced, chances for second marble are `1/4` i.e. assuming dlue marble has been already drawn.