Question

A diagnostic test for disease X correctly identifies the disease 94% of the time. False positives occur 14%. It is estimated that 0.95% of the population suffers from disease X. Suppose the test is applied to a random individual from the population. Compute the following probabilities. (It may help to draw a probability tree.)

The percentage chance that the test will be positive = %

The probability that, given a positive result, the person has disease X = %

The percentage chance that, given a negative result, the person does not have disease X = %

The percentage chance that, the person will be misclassified = %

Answer 1

The percentage chance that the test will be positive = 0.893+0.007 = 0.9 = 90%

The probability that, given a positive result, the person has disease X = 0.893/0.9 =99.22 %

The percentage chance that, given a negative result, the person does not have disease X =0.043/(0.057+0.043) = 0.43 = 43 %

The percentage chance that, the person will be misclassified = 0.057+0.007 = 0.064 = 6.4%