If a test for a disease has a sensitivity of 90% and a specificity of 95%, what is the probability that a person who tests positive actually has the disease, given that the prevalence is 1%? (2022)
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If a test for a disease has a sensitivity of 90% and a specificity of 95%, what is the probability that a person who tests positive actually has the disease, given that the prevalence is 1%? (2022)
Q: If a test for a disease has a sensitivity of 90% and a specificity of 95%, what is the probability that a person who tests positive actually has the disease, given that the prevalence is 1%? (2022)
Step 1: Understand the terms. Sensitivity is the probability that the test correctly identifies a person with the disease. Specificity is the probability that the test correctly identifies a person without the disease. Prevalence is the actual proportion of people in the population who have the disease.
Step 2: Write down the values given in the question. Sensitivity = 90% = 0.9, Specificity = 95% = 0.95, Prevalence = 1% = 0.01.
Step 3: Calculate the probability of having the disease given a positive test result using Bayes' theorem. The formula is: P(Disease | Positive) = (Sensitivity × Prevalence) / ((Sensitivity × Prevalence) + (1 - Specificity) × (1 - Prevalence)).
Step 4: Substitute the values into the formula. P(Disease | Positive) = (0.9 × 0.01) / ((0.9 × 0.01) + (0.05 × 0.99)).
Step 5: Calculate the numerator: 0.9 × 0.01 = 0.009.
