Probability of Simple Event - Complementary Events and examples

# Simple Events

An event in probability theory is referred to an experiment or a process. Simple events are those events where there is occurrence of a single event. Events can be different types such as simple events, compound events, complementary events, mutually exclusive events and so on. Simple events can be also classified as complementary events, mutually exclusive events and exhaustive events. The probability of simple events can be calculated as the ratio of number of favorable events and number of events in a sample space. Many times in real world we can find simple events whose probability can be calculated.

## Definition

Simple events are the events where one experiment happens at a time and it will be having a single outcome. The probability of simple events is denoted by P(E) where E is the event. The probability will lie between 0 and 1. For example, tossing of coin is a simple event. But if we are tossing a coin and rolling a die simultaneously then it will not be called a simple event as two events are occurring simultaneously.

## Probability of Simple Event

Probability of a simple event E is obtained as the ratio of number of favorable events to total number of events. For an event of tossing a coin, first we need to find the sample space. The sample space will be {H, T} as there are two possible events, to get a head or to get a tail. Now, to get a head and tail are simple events. The probability of getting a head will be ratio of favorable event and all events.

Favorable events, n(E) = {H} = 1

Probability, P(E) = $\frac{1}{2}$

## Complementary Events

Two simple events are known as complementary events if they are the only outcomes of a certain experiment. For example, if a bulb is on or off are complementary events as the bulb can either be on or off. Similarly, in tossing of a coin getting a head or a tail are complementary events. But while rolling a die, getting a 1 and getting a 6 are both simple events but they are not complimentary. If two complementary events are A and B, then P(A) + P(B) = 1, that is, sum of their probabilities will be 1.

## Real World Examples

We can find simple events in real world every now and then, and we can calculate their probability also.

1) Team A is playing match, then the event of the team winning the match is a simple event.

2) A bag is having 3 red and 5 green balls. The event of picking a ball in random and getting a red ball is a simple event.

3) Choosing a card from deck of 52 cards and getting a certain card.

4) Getting a random number from set of whole numbers or natural numbers. To get an even number will be a simple event.

5) A fan is hanging to the ceiling of a house and the event of the fan falling down will be classified as a simple event. The fan will fall down or not      fall down are complementary events
.