Assume there is a medical test to diagnose a disease. If a person has the diseas
ID: 3073680 • Letter: A
Question
Assume there is a medical test to diagnose a disease. If a person has the disease, the probability of having positive test result is 98 percent. If a person does not have the disease, the probability of having negative test results is 99.6 percent. The probability that a person has a disease is 1 percent in the population.
Answer the following questions:
a) If a person has a positive test result, what is the probability that he/she has the disease?
b) If a person has a positive test result, what is the probability that s/he doesn’t have the disease?
c) If a person has a negative test result, what is the probability that he/she doesn’t have the disease?
d) If a person has a negative test result, what is the probability that s/he has the disease?
Note: Use the following notation in your answer:
D: Person with disease
ND: Person without disease
+T: Positive test result
- T: Negative test result
Write each question in the form of mathematical notation for conditional probability.
Calculate the answer using two methods:
1. Bayes’ rule and conditional probability equations.
2. Draw a table, assume a population (e.g. 1 million) and provide numerical answers
Explanation / Answer
Has the disease Does not have the disease Total
Test positive 9800 3960 13760
Test negative 200 986040 986240
Total 10000 990000 1000000
a) P(has the disease | Test positive) = P(has the disease and test positive )/P(Test Positive)
= 9800/13760 = 0.7122
b) P(Doesn't have the disease | Test positive) = P(Doesn't have the disease and test positive)/P(Test positive) = 3960/13760 = 0.2878
c) P(Doesn't have the disease | Test negative) = P(Doesn't have the disease and test negative)/P(Test negative) = 986040/986240 = 0.9998
d) P(has the disease | Test negative) = P(has the disease and test negative)/P(Test negative)
= 200/986240 = 0.0002