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Chapter 3: Q. 37 (page 217)

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

Short Answer

Expert verified

The sum of an event's probability and its complement is1.

Step by step solution

01

Introduction

The term "probability" simply refers to the likelihood of something occurring. We may talk about the probabilities of particular outcomes鈥攈ow likely they are鈥攚hen we're unclear about the result of an event. Statistics is the study of occurrences guided by probability.
02

Explanation

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

Complement of event "A" is "not Anwhich 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(A)+PA'=1

Here,

P(A)=probability of the coin, coming to head.

PA'=probability of the coin, coming to tail.

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