Introduction

Events can be defined as a set of particular outcomes for any given random experiment being conducted. Collecting a set of all possible outcomes while performing a random experiment is called a sample space. The sample space can indicate all the possible outcomes of an experiment. So, in a way, events and sample space are related, and probability events can be considered the subsets of the sample space.

Calculating Events

Dividing the number of favourable outcomes by the total number of outcomes of any experiment can give us the likelihood of occurrence of events in probability. Generally, the probability of any event occurrence lies between 0 and 1. This suggests the possibility of more than one event associated with each sample space.

Example

Let us consider a fair dice roll. The total number of possible outcomes forms the sample space. It is given by {1, 2, 3, 4, 5, 6}. Now, let us consider an event, denoted by E, is defined as getting an odd number on the dice. Now, E = {1,3,5}. Thus, this explains that E is a subset of the sample space and is an outcome of the rolling of a dice.

Now let’s go for another example of flipping a coin. We all know that a coin has two sides, namely heads and tails. We have learned that the results of any given random experiment, also called events, are connected with the experiments. Thus, in this case, “heads” or “H” and “tails” or “T” are considered to be the results of this random experiment that provides an unbiased outcome.

Different Types of Events

 Some of the different types of events in probability are:

• Simple events
• Compound events
• Dependent Events
• Independent Events
• Impossible Events
• Sure Events
• Complementary Events
• Equally Likely Events

Examples of simple events

• If S is the sample space that contains any five samples and E is one of the events present in the space, then E is said to be a simple event.

S = {58, 73, 94, 87, 62} and E = 94.

• If a dice is thrown, the probability of getting 2 on the dice is a simple event and is given as E = {2}.

Impossible Events

 The term impossible is generally used to define anything that cannot occur, happen or exist. It is a sign of letting someone know that some things cannot be affected, performed, or achieved. Likewise, in this case, this refers to logically impossible events, or there is no chance of the particular event to occur. The probability for such specific events is given by 0. The empty set, denoted by Φ, is an impossible event.

Examples of impossible events

• The event of drawing a white ball from a bag containing two black and five red balls is impossible.
• Getting seven as the outcome in the throwing of a dice is impossible.

 Sure Events

 When an event is sure to occur or take place, it is termed a sure event. The chances of such events happening are highly likely and can occur at every experiment’s performance. This probability of occurrence of the sure event is 1. The sample space, denoted by S, is a sure event.

 Example of sure events

 If A is considered the event of getting a head or tail in a random experiment of tossing an unbiased coin, then A is said to be the sure event.

Dependent Events

Dependent events are termed to be events that depend on previous outcomes and results. Other events can affect the occurrence of these types of events.

 Examples of dependent events

• Drawing two balls one after another from a bag containing several balls without replacement.
• Drawing two cards from a deck without replacement. If we wish to draw an ace, the chances of drawing one are 4 out of 52 in the first attempt. However, it becomes more likely to draw an ace in the second attempt as fewer cards are available now.

Mutually Exclusive Events

The type of events that cannot coincide is termed mutually exclusive events. They do not have any common type of outcomes.

Examples of mutually exclusive events

• S = {5,4,3,2,1}, A = {5,4} and B = {3,2,1}. We can see that there is nothing common among the sets A and B. So, they are said to be mutually exclusive.
• A simple example is flipping a coin where the outcome is either heads or tails, but never both.

Conclusion

The different types of events in probability, such as simple and compound events, dependent and independent events, sure and impossible events, complementary and equally likely events, can be used per the sample space and the outcome we wish to attain. We use these concepts while playing cards, tossing a coin for cricket, or throwing a dice for a snake and ladder game.