What is the probability that at least 1 person has D?

Question

Consider a blood test for disease D. Assume that in population the

ratio
• of persons with D is 0.05,
• of positive test of persons with D is 0.97
• of negative tests of healty persons is 0.99
(a) Determine the probability
• of a positive test result and
• of D in case of a positive test result.
(b) 10 persons with a negative test result are selected at random.
What is the probability that at least 1 person has D?

Answer 1

a) 0,05*0.97 + 0,95*0,01

0,05*0,97/(0,05*0.97 + 0,95*0,01)

b) p(negativ) = p(n)= 0,95*0,99+0,05*0,03

-> 1- (1-(p(n))^10 = ...