Types of events

Types of events in probability and statistics:
There are various types of events in probability and statistics:

1. Simple event: If the event consists of less than 2 elements from the sample space then it is called a simple event or elementary event.

If sample space is S = 2, 3, 4, 5, 6.
And if event is E = 3, then it is a simple or elementary event.

1. Compound event: It comes under the types of events in probability and statistics as if the event consists of more than one element or sample points from the sample space then it is called a compound event.

If sample space of throwing a dice is, S = 1, 2, 3, 4, 5, 6.
And if event is, E = 1, 3, 5, then it is known as a compound event.

1. Sure event or certain event: It comes under the types of events in probability and statistics (for more visit this)as if the sample space is, S = 1, 2, 3, 4, 5, 6 and the event is also same as that of sample space, i.e., E= 1, 2, 3, 4, 5, 6 which is also the subset of S and it occurs whenever an experiment is performed. Therefore, the event E is called as a sure event or certain event.

1. Mutually exclusive events: It comes under the types of events in probability and statistics as  if we consider a random experiment of throwing a dice and sample space is, S=1, 2, 3, 4, 5, 6. Two events associated with the above experiment are called mutually exclusive if both the events cannot occur at the same time or in the same trial. Like A=1, 3, 5 and B=2, 4, 6 are mutually exclusive events. If the events are A = 1, 2, 4 and B= 2, 5, 6 are not mutually exclusive as 2 is favorable to both the events.

1. Exhaustive Events: It comes under the types of events in probability and statistics for any random experiment, S, E1, E2, E3,….En are the events which are the subsets of S.

E1, E2, E3,…..En are consider as exhaustive events if the union of all of them is equal to S, i.e.,
E1 U E2 U E3 U ….U En = S
The above equation also proves true if the set of events E1, E2,…En are mutually exclusive and exhaustive events.

1. Null event: This event is always added in the sample space as a sample point called φ(fi).  This event is the subset of S and is called as null event or impossible event.

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Probability and Statistics

Probability And Statistics : when we study in secondary school education Andhra Pradesh about the approaches of studying the theory of  Probability they are  Statistics approach and the classical approach of finding probability.  In statistics approach we find the probability of occurrence of an event by observing the repeated experiments and their frequency. Here we find the ratio of  the frequency of the event to be observes to the total frequency of the event which has been observed. Let us consider an event of throwing a coin. The possible outcomes of this event are Head and Tail, called as H and T.

The probability of getting a head on a throw of a coin will be the ratio of frequency of getting a Head to the total outcomes. Here we have total outcomes = 2 and the frequency of getting a head in total outcomes is 1. SO the probability of getting a head = 1/2. Similarly we can find the probability of getting a tail is also 1/2. This method of finding the probability applies to  the cards, dice, coins and other many simple games of chance. When we are diverted from these games of chance and consider the situations which are likely to occur like probability of people who will die before age of 60, probability of getting a rain this week. In such cases it is not possible to do simple enumeration of cases which are likely to occur.

In upcoming posts we will discuss about Types of events and Learn Pythagorean Theorem. Visit our website for information on Stem and Leaf Plot

Types of Events in Grade XI

Hi students, once again I am here to help you and to teach you an interesting math topic called as types of events in probability of Grade XI. You all have gone through the term probability. It describes the attitude of mind towards some proposition of whose truth we are not certain. Event is the outcome or a combination of outcomes of an experiment. in mathematical terms we can define this as a subset of a sample space. Example:

=> a head in the experiment of tossing a coin is an event.

=> a sum equal to 6 in the experiment of throwing a pair of dice is an event.

Now move to the occurrence of event, with help of an example (see for more Conditional Probability Examples), suppose we throw a die. Let ‘E’ be an event of a perfect number. Then E = 1, 4. Let on the upper most face 3 present. In this we say that event has not occurred. ‘E’ will occur only when 1 and 4 appear on the upper side. In a random problems, if E is the event of a sample space” > sample space S and w in the output. In this situation we can easily say that event E has occurred if w € E. Visit this site for more information on Probability.

Now move to different types of events: 

1. Simple Event

2. Compound Event 

3. Null Event

4. Sure Event or Certain Event

5. Compliment of an event

6. Mutually Exclusive Events 

7. Exhaustive Events 

1) Simple Event: it is defined, If an event has one element of the sample space">sample space. 

S= 1,2,3,4,5,6 

If the event is set of elements less than 2, then

E = 1 is a simple event

2) Compound Event: A compound event is an event which has more than one sample points. 

In the above example, of throwing a die, 1, 4 is a compound event.

3) Null Event (f): As null set is a subset of S, it is also an event called the null event or impossible event.

4) The sample space S= 1, 2, 3, 4, 5, 6 in the above experiment is a subset of S. The event represented by S occurs whenever the experiment is performed. Therefore, the event represented by S is called a sure event or certain event.

5) Complement of an Event: The complement of an event E with respect to S is the set of all the elements of S which are not in E. The complement of E is denoted by E' or EC.

In an experiment if E has not occurred then E' has occurred.

We can easily define union, intersection, complement of events and their properties in types of events.  like: 

 A U B, A ∩ A’ are events of the random experiments.

1. A – B is an event, which is same as “A but not B”.
2. A U B = B U A, A ∩ B, A ∩ B = A ∩ B
3. (A U B)’ = A ∩ B’, (A ∩ B)’ = A’ U B’ 

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