Independent

In probability, two events are said to be independent when the occurrence of one event does not make any effect on the other event. It means that any two related events that have no effect on each other. Here an event refers to any type of activity that is performed manually. In mathematical definition two events are independent if the outcome of one event does not make any influence in the outcome of second event. In the process of finding the probability of two independent events requires to multiply the probabilities of the two events. After obtaining the outcome, if needed then simplifies the final result.
Suppose the event of getting a Red heart in first attempt and the event of getting a black heart in second event are independent event. So, we can say that any two random variables are independent if the conditional probability distribution of either given the observed value of the other is the same as if the second event’s value had not been observed. The concept of independent event is most widely used in probability to give knowledge to the students of Grade VI. (know more about syllabus of cbse board, here)
In the form of standard definition independent events can be defined as:
Suppose we have two independent events x and y then they can be represented as
 P (x ∩ y) = P (x) . P (y),
In the above notation ‘x ∩ y’ can be defined as intersection of ‘x’ and ‘y’. It means that it is an event where both events ‘x’ and ‘y’ occur. In probability of independent events we can apply the multiplication rule that is given below:
Rule for probability of independent event:
If two events ‘x’ and ‘y’ is independent then probability of occurrence is:
   P (x and y) = P (x) . P (y),
In the next session we will discuss about Collect/organize/graph data. 

Representing probability

This unit is for the students of Grade VI; here we are going to learn probability representation. We come across the situations in our daily life when the results are unpredictable, like the toss of a coin, where we are not sure whether we will get a head or the tail. In day to day life we come across the statements like “Probably I may get the job next month”, “USA might win this one day cricket match series”. Such cases involve the elements of uncertainty or chance. A numerical measure of such   uncertainties is provided by a very important branch of statistics called the theory of probability. (know more about icse board syllabus, here)

Today this subject has been developed up to such extent that its use is seen in almost every field of life. This tool of measuring probability is used in social, physical science and in the quantitative analysis of all business and economics related problems. Statistics forms the basics of decision theory which means making decisions under the conditions of uncertainty. Representing probability basically means representation of the chances of probability of any event in forms of figures and numbers. When we want to find the probability of occurrence of any event, we must know the possible outcomes and the total number of outcomes of the experiment. It will be clearer with the following example. If you toss a coin and you need to know the probability of getting a head. It is absolutely uncertain event. When we flip a coin, we do not know if it will be a head or a tail. Now we know that there may be two possible outcomes H, T. So the possibility of getting a HEAD is 1 /2.
So the probability of getting a head is P (H) = ½.
 In the next session we are going to discuss Independent.