In a city 1% of population is actually suffering from covid 19. A laboratory test is 95% effective is detecting the disease when it was actually present. however lab test yeilds a false positive results for 0.5% of healthy person's test. A person was selected for test and test report was positive, find the probality he was not loving disease.

Asked by mike010thedanger | 11th Dec, 2020, 11:22: AM

Expert Answer:

Let E1 and E2 be the events that a person suffering from COVID-19 and a person not not suffering from COVID-19.
As per the question P(E1) = 1/100 = 0.01
Now, P(E1) + P(E2) = 1
P(E2) = 1 - P(E1) = 1 - 0.01 = 0.99
P(A|E1) = 99% = 0.95
P(A|E2) = 0.5% = 0.005
Probability that a person not loving disease, given that his test result is positive, is given by P(E2A).
By using Baye's theorem, we obtain
P(E2|A) = P(E2) P(A|E2)/{P(E1) P(A|E1) + P(E2) P(A|E2)}

Answered by Renu Varma | 14th Dec, 2020, 02:00: PM

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