Probability-Events

Introduction

To understand events in probability, we must first understand what probability is. Probability can be defined as the likeness of something happening. For example, if we draw a single card from a deck with a motive to draw an ace, its chance of being an ace of spades is its probability. 

In the above example, there will be a total of 52 possible outcomes. Let an event, E, be defined as drawing an ace. Then the event will be the set of all the aces in the card, i.e., E= {ace of spades, ace of diamond, ace of heart, ace of clubs}.

Events

Events in probability are a subset of outcomes that are likely to occur in a set of outcomes. We can understand it better through an example: if we roll a dice, then the set of outcomes that can occur is {1,2,3,4,5,6,}. We can define the event of getting an odd number as E. then E={1,3,5}. So we can say that E is the subset of the set of outcomes.

Types of events

Although there is only one set of outcomes from which events can occur, there are different types of events:

Independent Events 

These are the events whose outcomes are independent of the previous outcomes. Regardless of how many times we experiment. Rolling dice is an example of an independent event.

Dependent events

These are the events whose outcome is dependent on the previous outcome. Every time we experiment, the following outcome will be affected by the previous outcome—for example, drawing cards from a deck without replacing the last card.

Impossible events 

These are the events where the probability of occurrence of that event is zero, regardless of how many times the experiment is conducted. For example, the probability of getting a seven while rolling dice is impossible because the dice has only six outcomes {1,2,3,4,5,6}.

Sure event 

Sure events are events where there is only one outcome of the experiment, or we can say that the probability of an event occurring is always one. For example, if we drop a rock from a high place, it will always go down; it cannot go up no matter how many times we drop it. So the only outcome for the experiment is rock going down. 

Simple event

A simple event is an event that consists of only a single result. For example, getting an ace of spade while drawing a card from a deck this event has only one result.

Compound event 

Compound event design event that is a set of more than one result. For example, getting a diamond card while drawing a card from a deck. This event has 13 results.

Complementary events

Complementary events occur when there are only two sets of events, and if one of the events takes place, the other cannot occur. The sum of the probability of both events will always be one. For example, when you toss a coin, there are two possible events: we will get ahead or tail, we can’t get both, And the sum probability of getting head or tail is 1.

Mutually exclusive events 

These are the events that cannot occur in the same instant. If one occurs, then the other.

It will not occur. For example, one can both win or lose a game. If a person loses a game, he cannot win the game, or we cannot turn in both directions simultaneously whether we turn left or turn right.

Exhaustive Events

These are the sets of events where one of the events will occur every time the experiment is performed. When a coin is tossed, the set of events of the outcome being a head or a tail is an example of an exhaustive event.

Equally likely events

Equally likely events are those whose probability of occurring is equal to the probability of any other event in the experiment. For example, drawing a king of diamonds from a deck of cards here, the probability of drawing any other card from the deck will be the same as drawing a king of diamonds.

Events associated with ‘AND.’

When elements of two events intersect, their association with each other is represented by ‘AND.’

Events associated with ‘OR.’

When elements of two events intersect, total events of both elements are represented by ‘OR.’

How to determine the probability of an event?

To determine the probability of the events, we can follow the procedure mentioned below

• First, we have to determine the total number of possible outcomes in the experiment.
• For the next step, we have to determine the number of favorable outcomes.
• For the final step, we will divide the value we got in the second step by the value we got from our first step.
• Now we have the probability of the events.

Conclusion

In this study material, we have learned that probability can be defined as the likeness of something happening. Events in probability are a subset of outcomes that are likely to occur in a set of outcomes.

 Some important types of events are independent events, dependent events, impossible events, sure events, simple events, compound events, complementary events, mutually exclusive events, exhaustive events, equally likely events, events associated with ‘AND’.