Question

According to an article in a computer magazine $5.7 \%$ of all computers break down during their predicted lifespan, and $9.5 \%$ of all computers are infected by a virus. Furthermore, $92 \%$ of all computers that break down are infected by a virus. What is the probability that a computer that is infected by a virus breaks down?

Name: Problem 8, Chapter 6: An Introduction to Decision Theory
Uploaded: 2023-11-01T16:54:45-08:00
Channel: Keondre Parker
Description: According to an article in a computer magazine 5.7 % of all computers break down during their predicted lifespan, and 9.5 % of all computers are infected by a virus. Furthermore, 92 % of all computers that break down are infected by a virus. What is the probability that a computer that is infected by a virus breaks down?

   According to an article in a computer magazine $5.7 \%$ of all computers break down during their predicted lifespan, and $9.5 \%$ of all computers are infected by a virus. Furthermore, $92 \%$ of all computers that break down are infected by a virus. What is the probability that a computer that is infected by a virus breaks down?

An Introduction to Decision Theory

Martin Peterson 1st Edition

Chapter 6, Problem 8

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Solved by Expert Keondre Parker

11/01/2023

Step 1

Step 1: Let's define the events: - A: The event that a computer breaks down - B: The event that a computer is infected by a virus Show more…

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According to an article in a computer magazine $5.7 \%$ of all computers break down during their predicted lifespan, and $9.5 \%$ of all computers are infected by a virus. Furthermore, $92 \%$ of all computers that break down are infected by a virus. What is the probability that a computer that is infected by a virus breaks down?

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Key Concepts

Conditional Probability

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is expressed as P(A|B), meaning the probability of event A occurring given that event B has occurred. This concept is fundamental in problems where events are interdependent, allowing for more precise probability estimates based on known outcomes.

Bayes' Theorem

Bayes' Theorem is a powerful tool for updating the probability estimate of an event based on new evidence. It relates the conditional and marginal probabilities of events and is formulated as P(A|B) = [P(B|A) * P(A)] / P(B). This theorem is especially useful when the direct computation of a conditional probability is difficult, allowing one to reverse or adjust probabilities in light of additional information.

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