Types of Events in Probability

Introduction

Probability is a concept of mathematics that measures the chances of something happening. The occurrence of something is called an event, and the result is called the outcome. So, a set of outcomes that are the results of some experiments are called events. In other words, events form a part of the sample space. So they are a subset of the sample. In probability, many kinds of events have certain distinct types of relationships with the likelihood of occurrence. 

Events in probability

The likely outcomes of an experiment from the sample space are called events in probability. The probability of occurrence is always measured from 0 to 1 for any event. One sample space can include several events.

Types of events in probability

Even though there can be only one sample space for a particular experiment, the space can give rise to different types of events. Following are some types of events in probability:

• Impossible and sure events: Any event that can never happen is known as an impossible event. Since such an event will not occur, its probability is always 0. An example of such an event would be sound traveling in a vacuum or zero dividing a number and the quotient being a real number. On the other hand, a sure event is one that will definitely happen. The probability of such an event will always be 1. An example of such an event is the square of 2 is 4 or the moon revolving around the earth.
• Complementary events: When the probability of one event is one only and only if the probability of another event is zero, then the two are called complementary events. Simply put, when there are two events such that one can occur only if the other does not, the two events are called complementary to each other. If the probabilities of a complementary pair of events are added, the result is always 1.

An example of a complementary pair of events would be a coin landing on either heads or tails. One event can occur only when the other does not.

• Exhaustive events: The set of all possible events from a sample space from which one event will always occur is called exhaustive events. This means that all the outcomes for an experiment are exhaustive events because at least one of them will definitely happen. The heads or tails of a coin are exhaustive events since at least one of them definitely happens. 

Another example would be the die landing on a particular number. The outcome will be one of 1,2,3,4,5 or 6. So all these outcomes form the exhaustive events of rolling a die since one of them will compulsorily occur. So the sum of exhaustive events makes up the whole of the sample space. But this does not mean that all the events in the set of exhaustive events are equally likely to happen. Not all events in the set of exhaustive events share the same probability of occurrence. 

• Equally likely events: When the probability of events is equal, they are said to be equally likely events. For example, it is equally likely that the coin will land on heads as it is that it will land on tails. So the two events are equally likely events.
• Mutually exclusive events: Suppose there are two events such that one cannot occur if the other does, then the two events are said to be mutually exclusive. For example, suppose there is a sample space set S = {13,14,15,16,17,18,19} and there are two subsets A = {13,15,17} and B = {14,16,18}. The two subsets A and B do not have anything in common, so they are mutually exclusive.
• Simple and compound events: A result is a simple event if it is a single point from the sample space. For example, from a sample of 1,2,3,4,5,6, the occurrence of a result that is less than 2 can only be one and can be represented by the single number 1. If the event encompasses more than one result from the sample, then the event is said to be compound. For instance, the occurrence of a result that is less than 5 is a compound event since it can be anything from 1 to 4.  
• Independent and dependent events: When an event does not depend on the outcome of a previous event, then it is known as an independent result. The probability of the occurrence of an independent event will always be the same irrespective of the number of times the experiment has been carried out. The occurrences of a coin landing on heads or tails are independent events. On the other hand, dependent events are affected by the occurrence of some previous event.

Conclusion

Probability is used to calculate the likelihood of various events in a number of fields from meteorology to epidemiology. Meteorology scientists use probability to determine the chances of various weather phenomena. Epidemiologists can find out the chances of infection through different types of exposure. So formal probability calculations are used in several ways and in a wide variety of research.