Question 1191533: 9% of population has a symptom of a disease. If one tests a symptomatic person, probability of testing positive is p=0.78. If one tests a person without symptoms, the probability is p=0.06. If you test a random person what is the probability of the test returning positive results? What is the probability of a positive testing person actually having a disease?
Answer by ikleyn(52780)   (Show Source):
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9% of population has a symptom of a disease.
If one tests a symptomatic person, probability of testing positive is p=0.78.
If one tests a person without symptoms, the probability is p=0.06.
(a) If you test a random person what is the probability of the test returning positive results?
(b) What is the probability of a positive testing person actually having a disease?
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(a) A random person EITHER has symptoms of the disease with the probability 0.09
OR has no symptoms with the probability of 1 - 0.09 = 0.91.
If the person has symptoms of the desease, then he contributes 0.09*0.78 to the probability to get a positive test.
If the person has no symptoms of the desease, then he contributes 0.91*0.06 to the probability to get a positive test.
So, the total probability to get the positive test is
P = 0.09*0.78 + 0.91*0.06 = 0.1248. ANSWER
(b) This probability is 0.78, as stated in the problem. ANSWER
Solved.
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