Events - Simple and Compound | Independent & Dependent Events
An experiment can be called as a process or a happening which will lead to different outcomes. Different outcomes of an experiment are known as events. The probability of an event is the likelihood of occurrence of an event. Sample space is the set of all events of an experiment. Events can be classified in various ways depending on different characteristics. The first classification will be simple and compound events, then independent and dependent events, impossible and sure event. ALso, there are mutually exclusive and mutually exhaustive events.

Simple & Compound Events

Simple events are those events where only a single experiment is carried out. Tossing of a coin or rolling a dice are known as simple events. Simple events can be complementary to each other and independent or dependent on each other. Simple and compound events are broadly classified categories of events.

Compound events are those events which have more than one experiments occurring together. For example, rolling a dice and tossing a coin together will be known as a compound event. The sample space of compound events is obtained using lists, table and tree diagrams.

Independent & Dependent Events

Independent events are those events where the occurrence of one event will not affect the probability of occurrence of the other event. If A and B are two independent events then the probability of both A and B will be written as $P(A \text {and} B) = P(A).P(B)$. For example, if we toss a coin twice then the outcomes are independent of each other.

Dependent events are those where occurrence of one event will affect the other event. For example, if there are 3 red and 2 green balls in a bag and one green ball has been taken out then the probability of getting a green ball in next attempt will get affected.

Mutually Exclusive Events

Two events which cannot occur together are known as mutually exclusive events. For example, a bulb cannot be on and off at the same time. So, these events are mutually exclusive. If A and B are two mutually exclusive events then the probability of A or B happening is written as, $P(A \text {or} B) = P(A) + P(B)$. 

Impossible Event

If the probability of an event is zero then it will be known as an impossible event. The empty set $\phi $ is known as the impossible event. If the probability of an event is 1 then that event will definitely occur. Such event is known as sure event.

Exhaustive Events

Events which together exhaust the whole sample space are known as exhaustive events. For example, when we roll a die one event is to get all odd numbers and other is to get all even numbers. Both the events together will exhaust the whole sample space.

Sample space = {1,2,3,4,5,6}
Odd = {1, 3, 5}
Even = {2, 4, 6}

The union of odd and even events will add up to the sample space.