From the population of a city, a proportion of P0 = 0.001 are sick (infected with a virus) asymptomatic. There is a test method:
if the test is positive then we consider that the person is sick;
if the test is negative then we consider that the person is healthy;
However, the test also gives erroneous results.
P1 = 0.05 is the probability of a false positive test
P2 = 0.20 is the probability of a false negative test
Let's assume that an asymptomatic character (whom we will call X) takes the test and the result is positive.
a) Calculate the probability that X is sick and the probability that he is healthy.
b) In this case, if the result was positive, then X must redo the test after a few days. If this test is also positive, the probability that X is ill increases. Calculate what value this probability will have.
c) To determine how many consecutive tests that are all positive must be done by X in order for his confidence that he is sick to be greater than his confidence that he is healthy.
d) Patient Y knows for sure that he was sick, but now he seems to have recovered. In reality, only half of those who think they are cured are actually cured (p=0.5). How many consecutive negative tests must he have for the probability of being healthy to be greater than 80%?

Answer rating: 100% (QA)

Lets solve each part of the problem step by step a To calculate the probability that X is sick and the probability that he is healthy we can use Bayes theorem Lets denote S as the event of being sick ... View the full answer