If p(a)=0, then p(b/a)=p(b ∩ a)/p(a) p(a/b) =p(a ∩ b)/p(a),
This is called as conditional probability Formula.
If we have a condition p (y ∩ x) = 0, then the event is called Mutually Exclusive Events. And we need to remember that for mutually exclusive events the conditional probability will always be zero.
Let us understand concept of conditional probability with help of an example,
Example 1: If a card is drawn from a pack of 52 cards, and that card should be of heart, than Calculate The Probability that the card is greater than 3 and less than 6?
Solution: For finding the conditional probability, we need to have two events so we will assume that ‘a’ is the event for getting a card greater than 3 and less than 6 and ‘b’ will be the event of getting a card of heart. As we know that there are 13 heart card in a pack of 52 cards so
P (b) = 13,
Now the task is to calculate the probability of heart card greater than 3 and less than 6 so there will be only 2 cards, 5 and 6 which are greater than 3 and less than 6.
Now we need to find the black cards greater than 4 and less than 9.
So p (b ∩ a) = 2,
Now we will put that in the given formula we will get
P (x/y) =2/13,
This is the required probability for the given event.