Question 1061848: A certain virus infects one in every 500 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus.
What is the probability that a person has the virus given that they have tested positive.
What is the probability that a person does not have the virus given that they have tested negative.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Use 10000 people so 20 are ill.
==========T+=======T-=======Total
D+======18=======2=========20
D--======998======8982=====9980
Total======1016======8984==========10000
The table shows that of the 20 who have the disease, 18 test positive and 2 negative.
Of the 9980 who don't have the disease, 10% test positive and 90% negative.
If the person tests negative, and there are 8984 of them, there is a 8982/8984 chance they don't have the virus (99.98%)
If the person tests positive (1016), there is an 18/1016 chance they have the virus or 1.77%.
In general, there is a 0.2% chance of a randomly selected individual having the disease, and if they test positive, that has increased nearly 9-fold to 1.77%, which is still low. Because so many people don't have the disease, the fact that 10% of them test positive means that there will be a lot of false positive tests.
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