Blood Test detects the disease 98% of the time if patient is sick. However, give

Question

Blood Test detects the disease 98% of the time if patient is sick. However, gives false positive result 3% of the time when patient is healthy. Suppose 1 % of the population has the disease. Find P(an individual has the disease given that the test result is positive)? Find P(an individual don't have the disease given that the test result is positive) Find P(an individual has the disease given that the test result is negative)? Diagram and show all the probabilities on each branch - Make sure conditional probabilities are typed clear

Explanation / Answer

Let

D = has disease
P = tested positive

a)

As

P(P) = P(D) P(P|D) + P(D') P(P|D') = 0.01*0.98 + (1-0.01)*0.03 = 0.0395

Hence,

P(D|P) = P(D) P(P|D) / P(P) = 0.01*0.98/0.0395 = 0.248101266 [ANSWER]

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b)

Also,

P(D'|P) = P(D') P(P|D') / P(P) = (1-0.01)*0.03/0.0395 = 0.751898734 [ANSWER]

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c)

As

P(D|N) = P(D) P(N|D) / P(N)

Then

P(D|N) = 0.01*(1-0.98)/(1-0.0395) = 0.000208225 [ANSWER]

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