The latest worldwide virus has an infection rate of 0.1 % (that is, 1 in 1000 people actually have the virus). The chance that someone who has the virus tests positive is said to be 99 %. The chance that someone who does not have the virus tests negative is also said to be 99 %. What are the chances that someone who tests positive does not in fact have the virus (a “false positive”)?

Question

The latest worldwide virus has an infection rate of   0.1  % (that is,   1 in   1000 people actually have the virus). The chance that someone who has the virus tests positive is said to be   99  %. The chance that someone who does not have the virus tests negative is also said to be   99  %. What are the chances that someone who tests positive does not in fact have the virus (a “false positive”)?

Ciara Melton · Accepted Answer

Consider an example of   100000 men.Among   100000 men,   100 men contracted the virus and   99 will be tested positive.There are   99900 men without virus and among them   999 will be tested positive (chance of being false positive is   1  %) .So among   999  +  99  =  1098 men who are tested positive there are only   99 men who actually have the virus.

Daisy Patrick · Accepted Answer

You are about 100 times more likely to test positive if you have the virus than if you do not, but this is not commensurate with the prior improbability of having the virus (1000 to 1). The evidence isnt as extraordinary as the claim, to say it another way. Usually covid tests are applied when there are other reasons to believe you have the virus, like you have symptoms or you were in contact with an infected person, so the math changes a bit more in that case to what you would expect.

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