Types of events

In mathematics, the study of probability theory can be considered as a part of mathematics. In the probability theory we generally perform the calculation of finding the likelihood occurrence that is related to any particular event. It means to say that when an event occurring so many times; at that time we are not able to predict what will be the outcome at each and every time. So at that we use the concept of probability to find out the probability for outcome of any event.  In the simple we can say that probability is the most important concept of mathematics that deals with the calculation of likelihood of a given event’s occurrence. In probability theory, an event which is related to the probability can be expressed in the form of number range from one to zero.
 In the probability theory, anything that happens is named as events. It means to say that event is a term which is used to show the outcome on the occurrence of something. In the probability theory events can be categorized in different types of events. The Types of events are (a) independent event (b) dependent event.
Independent event: independent events are those events which has the no effect by any other type events. It means to say that the outcome of any event must not be dependent on another event. These events are considered as independent event. Suppose you toss a coin two times , in first it comes ‘tail’ then at that time you are not able to predict what will be the second outcome form the second toss. This thing is known as independent event.
Dependent event: Dependent events are those events whose outcome depends on outcome of another event. Suppose: there we select a card form a pack of card. The card is of heart of king. Now if we want to pick the next card then it will sure that the next card will not be king of heart. This event is known as dependent event.
In the next session we are going to discuss conditional probability, Grade IX.

conditional probability

In mathematics, probability can be considered as a branch of mathematics. The concept of probability deals with the calculation of the likelihood occurrence of any given event. The term probability describes their value in the range between 0 and 1. In the concept of probability the value one refers to the certainty of the occurrence of any particular event. In the same aspect the value zero refers to the impossibility of occurrence of any event. The basic behind using the concept of probability in mathematics is that when the lots of situations happens and we are not able to predict the outcome of the particular event then the concept of probability is used in this case to analyze the different possibilities and how likely each of them is. (know more about cbse board papers, here)
   There are various concepts are defined that helps in understanding the probability more clearly. Form that concepts conditional probability is one of them. In the probability theory, the conditional probability is a concept which defines the conditional relationship between two occurring events. It means to say that the conditional probability of ‘X’ given ‘Y’ is the probability of X if Y is known to occur. In the mathematical notation we can represent the conditional probability as P (X / Y).  It means to say that the conditional probability of occurrence an event Y is only when the occurrences of the event ‘X’ is already done.  In probability theory the definition of conditional probability can be represented by using formula for conditional probability:
       P (X / Y) = P (X and Y) / P (Y),
In the above definition of probability we need to remember one thing that the value of the P (Y) must be greater than zero. In most of the cases the P (X / Y) can be visualized as probability of event ‘X’ when the sample space of the event ‘Y’ is restricted. In the next session we will discuss about Permutations and combinations.