Let us consider any event E, which is associated to some of the random experiment and is occur if the occurrence of any one of the elementary event is its outcome. If S is a Sample Space and a random experiment is performed. Then if E is any event, it means E is the subset of S. Then the Probability of an occurrence of event E is defined as:
P (E) = number of distinct elements of Event E / Number of distinct elements of sample S. We also know that S includes all possible outcomes of the event.
Or we can write P (E) = n (E) / n (S)
Let us take some example to understand the concept more clearly. Let’s take a pot with 10 blue balls and 90 red balls, which are of similar shape and size. Let us first mix the balls thoroughly and then one ball is drawn from the pot randomly. We come to the conclusion that the ball taken out from the pot will be either of blue color or of red color. As the number of red balls is much more than the number of blue balls, so this is more likely to get a Red Ball in compare to the Blue Ball. So we can say that the probability of getting a red ball is more likely than the probability of getting a blue color ball. This means event which is more likely to occur has higher probability as compared to the event which has less possibility of occurrence. Here we first count the total number of events = 90 + 10 = 100. We say that the probability of an occurrence of an event of getting a red ball = P( Red Ball ) = 90 / 100. And the probability of an occurrence of an event of getting a blue ball = P ( Blue Ball) = 10 /100.
The addition theorem in the Probability concept is the process of determination of the probability that either event ‘A’ or event ‘B’ occurs or both occur. The notation between two events ‘A’ and ‘B’ the addition is denote...Read More
Mutually exclusive events are also called as incomparable events. Now let’s look at mutually exclusive events definition: Two or more events are called mutually exclusive events in such a case when we find that the occurrence of one of the event prevents the occurrence of the other events in the space. It also means that no two or more events can occur simultan...Read More
Let us consider n Elementary Events which are associated with any random experiment. Then their exist 2^n Subsets. Each subset of S is an event associated to the random experiment and the given Sample Space is the universal Set of these events. These 2^n events are divided into different types on the basis of their nature of occurrence. When we talk about a sure event, which ...Read More
Every subset of a Sample Space is called an event in language of Probability and Statistics. To every event which is associated with any random experiment, we try to attach any numerical value which is called the Probability. Any event associated with a random experiment is called an impossible event when we observe that this event does not occur at all when ever and ho...Read More
Any two events are called complementary if the event has only two possible outcomes. Let us consider a situation of throwing a coin. There are only two possible outcomes in this event, either we get a head or we get a tail. In such event we observe that at one time only one of the two events occur and besides these two events, no other event will occur. Such two eve...Read More
Any two or more events which occur in the space S and are associated with some random experiment are called exhaustive event if their Union forms a Sample Space. Exhaustive events Probability of the union of all the events is always 1. One case of a collectively exhaustive and mutually exclusive event is tossing a coin, whose likely results are Head or Tail. We observe...Read More
An example of an elementary event is to get the number 4 on the roll of a dice. As the word tells, elementary means only one. Thus, elementary event means the event which has only one outcome. This event is also termed as Atomic event. Any simplest type of event which we can ever talk about is an “elementary event" .It is the most basic type of event which we can talk ...Read More
The events which cannot be further divided to any smaller events are called Elementary Events or we can call it simple events
Let us consider any experiment ‘S’ of tossing a coin. We know that the possible outcomes of throwing a coin S = H, T.
In this expression, we observe that “ S “ is a Sample Space and “ H “ and “ T “ are the two elementary events of...Read More