Question

The test to detect the presence of a liver disorder is 98% accurate for a person having the disease and 97% accurate for a person not having the disease. If 3.5% of the people in a given population actually have the disorder, what is the probability that a randomly chosen person gets an incorrect diagnosis?

Answer 1

The probability tests to detect a liver disorder:
P (presence)= 0.98 (true)  0.02 (false)
P (absence)= 0.97 (true)  0.03 (false)

P(have disorder from the population)=0.035
P(do not have disorder from the population)= 0.965

To test positive:
P[have disorder and true from P(presence)] + P[do not have disorder and false from P(absence)]

=0.035*0.98+0.965*0.03= 0.06325

The answer is 0.06325

Answer 2

The answer is 0.06325