Composite Events: In the Field of Probability

Introduction

Composite events are those events that comprise an elementary events grouping. Its example could be the possible outcomes of all three coins whose tossing takes place together. The probability of composite events involves the combination of at least two simple events.

These are either the union or the intersection of two simple events. On tossing one coin only, the probability that the head will come is a simple event. However, on tossing two coins, the probability of getting both heads is a composite event as it involves the combination of two simple events. Keep reading to understand exactly what composite events are and their various aspects.

What are Composite Events?

Composite events are those whose subdivisions can take place into smaller events. This means that you can view these events in the form of smaller events. Similarly, you can also view them as a union of multiple events, two or more. They are also known as compound events.

So, for example, a person throws a die. Here, a composite event would be the event of getting an even number. Now, a further breaking down or sub-division of this composite event can take place into three simpler events as shown below:

• The event which gets 2
• The event which gets 4
• The event which gets 6

Probability of Composite Events

Experimental probability refers to the ratio of the proposed outcome to the experimental trials number.

P(success) = number of times the event takes place/total number of experiment trials 

The expression of the probability can take place as one of the following:

• A percentage
• A fraction
• A decimal
• A ratio

Composite events are two events of simple nature considered together. Their expression usually takes place as A and B.

Understanding Composite Probability

Composite probability is a term of mathematical nature whose relation is to the likeliness of two independent events taking place. It equals the probability of the first event multiplied by the second event’s probability. The use of such probabilities takes place by insurance underwriters for risk assessment and premiums assignment of insurance policies and products.

One of the best examples of compound probability is a case where a coin is flipped twice. Now, if we assume that the probability of attaining heads is 50%, then the expression of the probability of attaining heads in a row twice would be as:

 (.50 X .50), or .25 (25%)

A composite probability involves the combination of a minimum of two simple events. Such events are what experts call composite events. The probability that a coin will bring up heads when only a single coin is tossed is referred to as a simple event.

Types of Composite Events

There are two types of composite events in existence which are as follows:

• Mutually exclusive compound events
• Mutually inclusive compound events
  

Mutually Exclusive Events

A mutually exclusive compound event is one in which two events are not possible to take place simultaneously. These events cannot take place simultaneously. Suppose there are two mutually exclusive events, A and B, then the probability of the occurrence of either A or B would be the sum of their probabilities.

For example,  A coin is tossed to get either a head or a tail.

The formula, in such a case, about mutually exclusive events A or B probability is expressed as:

P(A or B) = P(A) + P(B)

Mutually Inclusive Events

Mutually inclusive events refer to cases where one event cannot occur with the other. Considering that there are two mutually inclusive events, A and B, then the probability of occurrence of either A or B taking place is the sum of their probabilities, minus the probability of occurrence of both the events. A non-empty intersection characterizes these events.

For example: Suppose an even number and a less than 5 number are picked. This would be a case of a mutually inclusive nature because 2 and 4 are even numbers and are below the value of 5.

The formula for the mutually inclusive events A and B probability is expressed as follows:

P(A or B) = P (A) + P (B) − P(A and B)

Conclusion

Composite events are those that involve an elementary events grouping. Its example could be the possible outcomes of all three coins when tossed together. There is a combination of at least two simple events in the probability of such events.

Understand the definition of composite events and what it implies carefully. After that, try to build an understanding of compound or composite probability. Afterward, move on to types of composite events. There are two types of such events: mutually exclusive and mutually inclusive events.