Question

A diagnostic test for a disease is such that it (correctly) detects the disease in 90% of the individuals who actually have the disease. Also, if a person does not have the disease, the test will report that he or she does not have it with probability .9. Only 1% of the population has the disease in question. If a person is chosen at random from the population and the diagnostic test indicates that she has the disease, what is the conditional probability that she does, in fact, have the disease?

Answer 1

TOPIC:Application of the Bayes' theorem.

- Define § C and the 2 T: following events as - Actually having the disease; The test detects the disease. Given that XP (The test detects Actually I the disease having the = 0.90 disease, (in decimals) => P (T 12) = 0.90 Again, we have, XP The test doesn't Not having - = 0.g. doteat the disease the disease -|(740) -0,3) - (- laganeleri (of having the disease) = 0.01. (in deci Алло, - P (DC) = 1 - P(A). [ Law of complemen- al-0.01. 9 P (44= 0.99

. We need to find Р/ Actually having the disease The test detects the disease = P (217). P (2). P (T12 P().P(TIM) +P (09). P(1/29 Bayes! theorem) 0.01 x 0.90 0.01 XO.90 + o.gg x Criven годаl/ I 0.1 - 2 1/12 10.0833 (in four decimais) (Answert