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If a disease has a 15% prevalence in a population and a test has a 95% specifici

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Question: If a disease has a 15% prevalence in a population and a test has a 95% specificity, what is the probability of a false positive result? (2021)

Options:

  1. 0.05
  2. 0.15
  3. 0.20
  4. 0.25

Correct Answer: 0.05

Exam Year: 2021

Solution: 

The probability of a false positive is equal to 1 - specificity = 1 - 0.95 = 0.05.

If a disease has a 15% prevalence in a population and a test has a 95% specifici

Practice Questions

Q1
If a disease has a 15% prevalence in a population and a test has a 95% specificity, what is the probability of a false positive result? (2021)
  1. 0.05
  2. 0.15
  3. 0.20
  4. 0.25

Questions & Step-by-Step Solutions

If a disease has a 15% prevalence in a population and a test has a 95% specificity, what is the probability of a false positive result? (2021)
  • Step 1: Understand what specificity means. Specificity is the ability of a test to correctly identify those without the disease. A specificity of 95% means that 95% of the time, the test will correctly show a negative result for people who do not have the disease.
  • Step 2: Determine the probability of a false positive. A false positive occurs when the test incorrectly indicates that a person has the disease when they do not. This is calculated as 1 minus the specificity.
  • Step 3: Calculate the probability of a false positive. Since the specificity is 95%, we convert this to a decimal: 0.95. Now, we subtract this from 1: 1 - 0.95 = 0.05.
  • Step 4: Interpret the result. The probability of a false positive result is 0.05, which means there is a 5% chance that the test will incorrectly indicate a person has the disease when they do not.
  • Prevalence – The proportion of a population found to have a condition.
  • Specificity – The ability of a test to correctly identify those without the disease (true negative rate).
  • False Positive Rate – The probability that a test incorrectly indicates the presence of a disease when it is not present.
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