Suppose 5% of the population have a certain disease.A laboratory blood test gives a positive reading for 95% of people who have the disease and 10% positive reading of people who do not have the disease.What is the probability of testing positive?
A)0.0475
B)0.1425
C)0.95
D)0.9
E)0.3333

Question

Quizplus · Accepted Answer

The probability of testing positive can be calculated using the law of total probability. Let's denote:- $P(D) = 0.05$ as the probability of having the disease,- $P(\neg D) = 0.95$ as the probability of not having the disease,- $P(+|D) = 0.95$ as the probability of testing positive given that the person has the disease,- $P(+|\neg D) = 0.10$ as the probability of testing positive given that the person does not have the disease.The total probability of testing positive, $P(+)$, is given by:$$P(+) = P(+|D)P(D) + P(+|\neg D)P(\neg D)$$$$P(+) = (0.95)(0.05) + (0.10)(0.95)$$$$P(+) = 0.0475 + 0.095 = 0.1425$$

Suppose 5% of the Population Have a Certain Disease