Use Bayes' Theorem to Find the Indicated Probability

question 109

Multiple Choice

Use Bayes' theorem to find the indicated probability.
-3.6% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 95.3% of those who have the disease test positive. However 4.2% of those who do not have the disease also test positive (false positives) . A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive?

• A) 0.847
• B) 0.036
• C) 0.541
• D) 0.459

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Definitions:

Reinforcement Theory

A psychological concept suggesting that behavior is shaped and conditioned by its consequences, with positive outcomes reinforcing the behavior and increasing its likelihood of recurrence.

Positive Consequences

Favorable outcomes or benefits that result from a specific behavior or action, often reinforcing the behavior.

Theoretical Frameworks

Structures of concepts, assumptions, and their relations, used to support or guide research, providing a comprehensive understanding of a phenomenon.

Performance Appraisals

The systematic evaluation of an employee's job performance and productivity, typically to determine compensation, promotions, and training needs.