Suppose that 1% of the population have a disease called stataphobia. There is a

Question

Suppose that 1% of the population have a disease called stataphobia. There is a diagnostic test with 0.95 probability of being positive when a person has stataphobia and 0.8 probability of being negative when a person does not have stataphobia. If a person tests positive for stataphobia, what is the probability they have stataphobia? step 1 define notation D- T- testing positive for stataphobia step 2 Identify probabilities given. There are three probabilities given in the question (0.01, 0.95, and 0.8). Which probabilities are these? having stataphobia step 3 Identify the probability you are asked to find. What probability is the question asking you to find? step 4 Use probability rules to find the probability you identified in step 3.

Explanation / Answer

step 1: let event D =having stataphobia and T =testing postive

step 2:

here probability of stataphobia =P(D) =0.01

probability of test positive given  stataphobia =P(T|D) =0.95

probability of test negative given not stataphobia =P(Tc|Dc) =0.8

step 3: required probability is having stataphobia given test positive =P(D|T)

step 4: probability =P(D|T) =(P(D)*P(T|D))/(P(D)*P(T|D)+P(Dc)*P(T|Dc))

=(0.01*0.95)/(0.01*0.95+(1-0.01)*(1-0.8))=0.0458

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