Question

How do you know if an event is dependent or independent?

Answer 1

Dependent event

Dependent events are those events that are affected by the outcomes of events that had already occurred previously. i.e. two or more events that depend on one another are known as dependent events. Dependent events are the events that affect the probability of the other event. It means that the outcome of the event gets influenced by the other event.

Independent Event

Independent events are those events whose occurrence is not dependent on any other event. If the probability of occurrence of an event $A$ is not affected by the occurrence of another event $B$, then $A$and $B$ are said to be independent events.

How to know if an event is dependent or independent

$A$ and $B$ are two events associated with the same random experiment, then $A$ and $B$ are known as independent events if $\mathit{P}\mathbf{(}\mathit{A}\mathbf{\cap }\mathit{B}\mathbf{)}\mathbf{=}\mathit{P}\mathbf{\left(}\mathit{A}\mathbf{\right)}\mathit{P}\mathbf{\left(}\mathit{B}\mathbf{\right)}$.