Conditional Probability in Grade X

Today , we are going to discuss about the topic conditional Probability, which you need to study at Grade X. Whenever we deal with conditional Probability, we have to deal with two events, let’s suppose these events are x and y. It can happen that these two events are related to each other. And if now we will be asked to calculate the probability then we need to check that event has occurred or not. We can define conditional Probability as the probability of an x if y is already occurred. We can calculate the conditional Probability of any two events by the formula given below.

If p(x)=0, then p(y/x)=p(y ∩ x)/p(x)   p(x/y)  =p(x ∩ y)/p(x)

This is called as conditional Probability formula.

If we have two mutually exclusive even, then p(y ∩ x)=0

In the case of mutually exclusive event then conditional probability is 0.

Now we will see some examples related to how to find conditional Probability?

Example 1: A card is drawn from a pack of 52 card, and we are told that the card is black, now find the probability that the card drawn is greater than 4 and less than 9?

Solution:

 Let x be the event for getting card greater than 4 and less than 9 and y be the event of getting black card. Now we need to find the probability of x when y is occurred, so we need to find p(x/y).

A pack of card contains 26 red cards and 26 black cards. And we need so collect the black cards, so p(x)=26

Now we need to find the black cards greater than 4 and less than 9.

As we know that in 26 black cards there will be 2 pairs of cards between 4 to 9. Now if we calculate then there will be 4+4=8cards

So p(y ∩ x)=8

Now we will put that in the given formula we will get

 p(x/y)=8/26

p(x/y)=4/13

This is the required probability for the given event. (To get help on cbse maths syllabus click here)

In the next topic we are going to discuss Statistical methods to make inferences and In the next session we will discuss about Data representation methods.