Use Bayes' Theorem to Find the Indicated Probability

question 152

Multiple Choice

Use Bayes' theorem to find the indicated probability.
-3.8% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% 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) 0.038
• B) 0.475
• C) 0.525
• D) 0.905

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Definitions:

Random Phenomenon

A random phenomenon is a natural or physical event that has an unpredictable outcome, with individual occurrences varying in a non-deterministic manner.

Probability

A numeric evaluation of the chance that an event will happen, specified as a number from 0 to 1.

Law of Large Numbers

A principle that states that as a sample size grows, its mean will get closer to the average of the whole population.

Probability Assignment Rule

A principle used to assign probabilities to outcomes of a random experiment, ensuring the probabilities are non-negative and sum to one.