In a population Ω, two diseases D1 and D2 are present in 10% and 20% respectively. It is assumed that the number of those who suffer from both diseases is negligible. We undertake a screening system of D1 and D2 diseases. To do this, we apply a test that works on 90% of D1 patients, on 70% of D2 patients, and in 10% of individuals who have neither of these two conditions. 1. When we randomly choose an individual ω in Ω, what is the probability that the test will work? 2. Knowing that for an individual ω, the test reacted, give the probabilities: a) So that the test reacted because of the D1 disease. b)So that the test reacted because of the D2 disease. c) So that the test reacted when the indiv
Problem8:
In a population Ω, two diseases D1 and D2 are present in 10% and 20% respectively. It is assumed that the number of those who suffer from both diseases is negligible. We undertake a screening system of D1 and D2 diseases. To do this, we apply a test that works on 90% of D1 patients, on 70% of D2 patients, and in 10% of individuals who have neither of these two conditions.
1. When we randomly choose an individual ω in Ω, what is the probability
that the test will work?
2. Knowing that for an individual ω, the test reacted, give the probabilities:
a) So that the test reacted because of the D1 disease.
b)So that the test reacted because of the D2 disease.
c) So that the test reacted when the individual was infected with neither
of the two diseases D1 and D2.
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