Consider the following situation... Suppose that 0.10% of the population suffers
ID: 3307181 • Letter: C
Question
Consider the following situation... Suppose that 0.10% of the population suffers from a particular serious disease and a test has been developed to diagnose the illness. The probability that the test correctly identifies someone who has the illness as positive is 0.98. The probability that the test correctly identifies someone who does not have the illness as negative is 0.94. You want to evaluate the effectiveness of this test, in particular (1) the probability of not having the illness when the test is negative and (2) the probability of having the illness when the test is positive. Based on these results, discuss the effectiveness of the test (don't just state "it's good or "it's not good" .Explanation / Answer
1) probability of test is negative=P( have disease and test negative+do not have disease and test negative)
=0.001*(1-0.98)+(1-0.001)*0.94=0.93908
therefore probability of not having disease when test is negative
=P(do not have disease and test negative)/P( test negative)=(1-0.001)*0.94/0.93908 =0.999979
2) probability of test positive =1-P( test negatice)= 1-0.93908 =0.06092
hence probability of having the illness given test is positive
=P(having the illness and test positive)P(test positive)=0.001*0.98/0.06092=0.016087
from above as test performs poorly in identifying the disease while it is not there; the test is not effective and needs to be done multiple time to increase relaibility of information