Question

According to the U.S. Census Bureau, the probability a randomly selected individual in the United States earns more than $\$ 75,000$ per year is $18.4 \% .$ The probability a randomly selected individual in the United States earns more than $\$ 75,000$ per year, given that the individual has earned a bachelor's degree, is $35.0 \%$. Are the events "earn more than $\$ 75,000$ per year" and "earned a bachelor's degree" independent?

Name: Problem 9, Chapter 5: Fundamentals of Statistics
Uploaded: 2021-06-18T06:09:54-08:00
Duration: 1 min 50 s
Channel: Manisha Sarker

   According to the U.S. Census Bureau, the probability a randomly selected individual in the United States earns more than $\$ 75,000$ per year is $18.4 \% .$ The probability a randomly selected individual in the United States earns more than $\$ 75,000$ per year, given that the individual has earned a bachelor's degree, is $35.0 \%$. Are the events "earn more than $\$ 75,000$ per year" and "earned a bachelor's degree" independent?

Fundamentals of Statistics

Michael Sullivan III 5th Edition

Chapter 5, Problem 9

Instant Answer

Solved by Expert Manisha Sarker

06/18/2021

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Let E be the event "earn more than $75,000 per year" and B be the event "earned a bachelor's degree". Show more…

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According to the U.S. Census Bureau, the probability a randomly selected individual in the United States earns more than $\$ 75,000$ per year is $18.4 \% .$ The probability a randomly selected individual in the United States earns more than $\$ 75,000$ per year, given that the individual has earned a bachelor's degree, is $35.0 \%$. Are the events "earn more than $\$ 75,000$ per year" and "earned a bachelor's degree" independent?

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Key Concepts

Statistical Independence

Statistical independence is a fundamental concept in probability theory where two events are considered independent if the occurrence of one event does not affect the probability of the occurrence of the other. This is mathematically expressed as P(A ? B) = P(A) * P(B), or equivalently, P(A | B) = P(A).

Conditional Probability

Conditional probability refers to the probability of an event occurring given that another event has already occurred. It is calculated using the formula P(A | B) = P(A ? B) / P(B). This concept is crucial when examining the relationship between two events to determine if they are independent or if one event influences the likelihood of the other occurring.

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