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Probability
NCERT Class 12
CBSE
Grade 12

Question:

A laboratory blood test is 99% effective in detecting a certain disease when it is in fact present. However, the test also yields a false positive result for 0.5% of the healthy person tested. If 0.1% of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?

Step-by-Step Solution

$P(E_1)=0.001, P(E_2)=0.999, P(A|E_1)=0.99, P(A|E_2)=0.005$. [1.0 Mark]
Bayes' formula: $\dfrac{0.00099}{0.00099 + 0.004995}$. [1.0 Mark]
$= \dfrac{22}{133}$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Identifying prior and likelihood values: 1.0 Mark
Formulating Bayes' fraction: 1.0 Mark
Evaluating probability $= 22/133$: 1.0 Mark

Correct Answer:
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