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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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Most popular questions from this chapter

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 64stamped, addressed envelopes with $10cash in different classrooms on the George Washington campus. 44%were returned overall. From the economics classes 56%of the envelopes were returned. From the business, psychology, and history classes 31%were returned.

Let:R = money returned;E = economics classes; O = other classes

a. Write a probability statement for the overall percent of money returned.

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e. Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. Include numbers to justify your answer.

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d. Are B and D mutually exclusive?

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