dependent

Probability can be considered as a branch of mathematics that deals with the calculation of likelihood of a given event’s occurrence. The occurrence of an event can be described in terms of number between the 1 and o. In the terms of probability, an event with a probability of 1 can be describe as certain or in the same aspect the probability of .5 can be specify as a half odd or half even. In the probability, an event is word which can be defined as a particular work which is performed in continues time period. When an event is performed in a particular time period then to estimate the outcome of that event, we use the concept of probability.
In the simple form we can say that when the number of occurring events is divide by the total number of events plus the number of failure of occurrence are known as probability. In the probability, some of the cases occur which has the two events. It means that in the probability some time two events are performed together at a time. On the basis of probability we can categorized the events in two ways, which are given below:
A)      Dependent event
B)      Independent event
Dependent events = Dependents are those events in which outcome of the one event affects the outcome of another event. It means to say that the output of the one event depends on the output of another event.
Independent events: independents events are those events which are independent to each other. It means that the outcome of one event not affect the outcome of another event. (know more about cbse sample papers for class 10, here)

Example: Suppose there is pack of playing card. If in case we pick card of king of heart. In the next time if we pick the card then it is obvious that card is not same to the king of heart. So, we can say that here both events are dependent to each other because in a Dependent Events Probability of the pack of card, there is only one king of heart exists.  In the next session we will discuss about Informal and mathematical language. 

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.