An event is a specific outcome or a collection of outcomes from a random experiment. For examples:- Tossing of a coin is a trail or random experiment, and getting of a head or tail is an event.
The types of events are:
- Simple and compound events
- Mutually exclusive events
- Equally likely events
- Exhaustive events
- Favourable events
- Independent and dependent events
‣ Simple and compound events:
An event that consists of a single outcome is called simple event (or elementary event). For example:- rolling a die and getting a 3 is a simple event.
A compound event is a combination of two or more simple events. For example:- rolling a die and getting a 3 is a simple event and the event of getting prime numbers (2 or 3 or 5) is a compound event.
• It is also know as composite or mixed event.
‣ Mutually exclusive events:
Mutually exclusive events are events that cannot occur at the same time. If one event happens, the other cannot. For instance, when flipping a coin, the events “getting heads” and “getting tails” are mutually exclusive.
‣ Equally likely events:
Equally likely events are events where each outcome has the same probability of occurring. For example, rolling any number on a fair die is an equally likely event because each number has a probability of 1/6.
‣ Exhaustive events:
The total number of all possible outcomes of a random experiment is called the exhaustive events.
For example:-
- In case of a fair coin, the total number of possible outcomes = 2
- If two coins are tossed simultaneously, then total number of possible outcomes = 4
- In throw of a fair dice, the total number of possible outcomes = 6
‣ Favourable events:
Favourable events are those outcomes that satisfy a specific condition or criteria. For example, in rolling a six-sided die, the event “getting a number greater than 4” has the favourable outcomes 5 and 6.
‣ Independent and dependent events:
Independent events are events where the occurrence or non-occurrence of one event does not affect the probability of the other event. For instance, drawing a red card from a deck and rolling a six on a die are often independent events.
Dependent events are events where the occurrence or non-occurrence of one event influences the probability of the other event. For example, drawing a red card from a deck of cards and then drawing another red card without replacing the first card are dependent events, because removing the first red card reduces the probability of drawing another red card.
