Question

What is the sum of the probabilities of an event and its complement?

Short answer

The sum of an event's probability and its complement is$1.$

Step-by-step solution

Introduction

The term "probability" simply refers to the likelihood of something occurring. We may talk about the probabilities of particular outcomes—how likely they are—when we're unclear about the result of an event. Statistics is the study of occurrences guided by probability.

Explanation

The sum of an event and its complement is always equal to $1$.

Complement of event "A" is "not $A^n$which is denoted by $A^{*}$.

Let us consider it with the example. Let us consider that for a coin, if the result is head then the complement will be tail. So as per the rule, the sum of the probabilities should be coming to one.

Hence, we can write as : $P\left(A\right)+P\left(A^{\text{'}}\right)=1$

Here,

$P\left(A\right)=$probability of the coin, coming to head.

$P\left(A^{\text{'}}\right)=$probability of the coin, coming to tail.