Question

According to the study mentioned in Exercise $87,^{56}$ the probability that a ground meat sample was contaminated by salmonella was . $20 .$ The probability that a salmonellacontaminated sample was contaminated by a strain resistant to at least one antibiotic was .84. What was the probability that a ground meat sample was contaminated by a strain of salmonella resistant to at least one antibiotic?

Name: Problem 94, Chapter 7: Finite Mathematics and Applied Calculus
Uploaded: 2021-12-07T20:57:22-08:00
Duration: 1 min 5 s
Channel: Lucas Finney
Description: According to the study mentioned in Exercise 87,^56 the probability that a ground meat sample was contaminated by salmonella was . 20 . The probability that a salmonellacontaminated sample was contaminated by a strain resistant to at least one antibiotic was .84. What was the probability that a ground meat sample was contaminated by a strain of salmonella resistant to at least one antibiotic?

   According to the study mentioned in Exercise $87,^{56}$ the probability that a ground meat sample was contaminated by salmonella was . $20 .$ The probability that a salmonellacontaminated sample was contaminated by a strain resistant to at least one antibiotic was .84. What was the probability that a ground meat sample was contaminated by a strain of salmonella resistant to at least one antibiotic?

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 5th Edition

Chapter 7, Problem 94

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Solved by Expert Lucas Finney

12/07/2021

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According to the study, the probability that a ground meat sample was contaminated by Salmonella, denoted as P(S), is 0.2. The probability that a Salmonella contaminated sample was contaminated by a strain resistant to at least one antibiotic, denoted as P(R|S), Show more…

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According to the study mentioned in Exercise $87,^{56}$ the probability that a ground meat sample was contaminated by salmonella was . $20 .$ The probability that a salmonellacontaminated sample was contaminated by a strain resistant to at least one antibiotic was .84. What was the probability that a ground meat sample was contaminated by a strain of salmonella resistant to at least one antibiotic?

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Key Concepts

Multiplication Rule

The multiplication rule states that the joint probability of two events occurring together is the product of the probability of one event and the conditional probability of the second event given that the first event occurred. This is expressed as P(A and B) = P(A) * P(B|A) and is fundamental when combining dependent probabilities.

Joint Probability

Joint probability is the probability that two events happen at the same time. It is calculated using the multiplication rule, particularly when the probability of one event depends on the occurrence of a preceding event.

Conditional Probability

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is represented as P(B|A) and is essential in situations where the probability of one event depends on the occurrence of another.

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