A blood test indicates the presence of a particular disease 96% of the time when the disease is actually present. The same test indicates the presence of the disease 0.5% of the time when the disease is not present Four percent of the population actually has the disease. Calculate the probability that a person has the disease, given that the test indicates the presence of the disease. Choose the correct answer below OA.. 0.889 OB. 0.95 OC. 0.167 OD. 0.96 IZD

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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**Transcription for Educational Website**

### Understanding Test Accuracy and Probability

A blood test indicates the presence of a particular disease 96% of the time when the disease is actually present. The same test indicates the presence of the disease 0.5% of the time when the disease is not present. Four percent of the population actually has the disease. Calculate the probability that a person has the disease, given that the test indicates the presence of the disease.

**Choose the correct answer below:**

- A. 0.889
- B. 0.95
- C. 0.167
- D. 0.96

### Explanation:

This problem is related to conditional probability and involves calculating the probability of having the disease given a positive test result. To solve this, you would use Bayes' Theorem, which is a key concept in statistics for such problems.
Transcribed Image Text:**Transcription for Educational Website** ### Understanding Test Accuracy and Probability A blood test indicates the presence of a particular disease 96% of the time when the disease is actually present. The same test indicates the presence of the disease 0.5% of the time when the disease is not present. Four percent of the population actually has the disease. Calculate the probability that a person has the disease, given that the test indicates the presence of the disease. **Choose the correct answer below:** - A. 0.889 - B. 0.95 - C. 0.167 - D. 0.96 ### Explanation: This problem is related to conditional probability and involves calculating the probability of having the disease given a positive test result. To solve this, you would use Bayes' Theorem, which is a key concept in statistics for such problems.
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