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Answer:
A)The probability that someone who tests positive has the disease is 0.9995
B)The probability that someone who tests negative does not have the disease is 0.99999
Step-by-step explanation:
Let D be the event that a person has a disease
Let be the event that a person don't have a disease
Let A be the event that a person is tested positive for that disease.
P(D|A) = Probability that someone has a disease given that he tests positive.
We are given that There is an excellent test for the disease; 98.8% of the people with the disease test positive
So, P(A|D)=probability that a person is tested positive given he has a disease = 0.988
We are also given that one person in 10,000 people has a rare genetic disease.
So,
Only 0.4% of the people who don't have it test positive.
= probability that a person is tested positive given he don't have a disease = 0.004
Formula:
P(D|A)==0.9995
P(D|A)=
A)The probability that someone who tests positive has the disease is 0.9995
(B)
=probability that someone does not have disease given that he tests negative
=probability that a person tests negative given that he does not have disease =1-0.004
=0.996
=probability that a person tests negative given that he has a disease =1-0.988=0.012
Formula:
B)The probability that someone who tests negative does not have the disease is 0.99999