TYPES OF EVENTS IN PROBABILITY

A group of outcomes of a random experiment can be defined as an event in probability. All possible results of an experiment are represented by the sample space. As a result, in probability, occurrences can be thought of as subsets of the sample space.

Probability events are the results of random experimentation. In probability, any subset of the sample space will produce events. The number of favourable results divided by the total number of outcomes of the experiment can be used to calculate the probability of events occurring. In probability, there are many different sorts of events. Each type of event has its own set of characteristics. This method of categorising events in likelihood aids in the reduction of mathematical calculations.

Definition of events in probability:- 

In probability, events are defined as a subset of a finite sample space that contains certain likely outcomes of an experiment. Any event’s chance of occurrence will always be between 0 and 1. A single sample space could be associated with a large number of events.

For example, Assume you’ve rolled a fair die. The sample space is made up of the total number of possible outcomes, which are represented by the numbers 1, 2, 3, 4, 5, and 6. Allow E to be defined as landing on an even number on the dice. Then E = { 2, 4, 6 }  is the answer. As a result, it can be observed that E is a subset of the sample space and is the result of a die roll.

Different types of events in probability:- 

In probability, there are various different sorts of events. For a random experiment, there can only be one sample space, but there can be many different sorts of events. The following are some of the most significant occurrences in probability.

Dependent and independent events:-

Independent events

In probability, independent occurrences are those whose outcome is not contingent on the outcome of a prior event. The likelihood of independent occurrences occurring is the same no matter how many times an experiment is repeated. Tossing a coin, for example, is an independent event in probability.

Dependent events 

In probability, dependent events are those whose fate is determined by the occurrence of a previous event. This means that the likelihood of a dependent event occurring is influenced by a previous outcome. Drawing two balls from a bag one after the other without replacing them, for example.

Impossible and sure event:-

Impossible event

The term “impossible event” refers to an occurrence that will never happen. Because impossible events in probability will never happen, the likelihood of them happening is always zero. The sun, for example, rotating around the earth is an impossibility.

Sure event

A certain event is one that will occur at some point in the future. A certain event’s probability of occurrence will always be 1. The earth’s rotation around the sun, for example, is a certain occurrence.

Simple and compound events:-

Simple event

A simple event is one that consists of a single point or a single outcome from the sample space. The simple event of rolling a fair dice and obtaining less than 2, written as E = 1, is an example of a simple event.

Compound event

A compound event is defined as one that comprises of more than one result from the sample space. In probability, rolling a fair die and getting an odd number is an example of a compound occurrence. E = 1, 3, and 5.

Complementary events:-

Complementary events in probability are two events that can only happen if and only if the other doesn’t happen. The total of complementing occurrences’ probabilities will always equal one. Suppose that E is defined as receiving a head when flipping a coin. The complement of E is thus E’, which represents the event of obtaining a tail. As a result, E and E’ are complimentary occurrences. These activities are mutually exclusive and exhaustive.

Mutually exclusive events:-

Mutually exclusive occurrences are those that cannot happen at the same moment. In probability, mutually exclusive events do not have any common outcomes. S = { 10, 9, 8, 7, 6, 5, 4 } A = { 4, 6, 7 } and B = { 10, 9, 8 } are some examples. Because sets A and B have nothing in common, they are mutually exclusive events.

Exhaustive events:-

Exhaustive events in probability are those that can be gathered from a random experiment’s sample space. In other words, exhaustive events are a set of occurrences from which at least one is certain to occur when the experiment is carried out. An exam, for example, has two outcomes: passing or failing.

Equally likely events:-

In probability, equally likely events are ones with equally likely outcomes. Getting a head or a tail on a coin flip, for example, are both equally likely outcomes.

These are some types of events that we have discussed.

Conclusion:-

A group of outcomes from an experiment can be defined as a probability event. To put it another way, a probability event is a subset of the sample space in question. A random experiment’s sample space, or individual space, is the whole collection of possible results. Any given event has a chance of 0 to 1.