So, to recognise that, I thought you might be interested in the following:
Suppose there is a medical test that is designed to detect whether you have an illness/infection/whatever.
Suppose the chance of anyone actually having that illness/infection/whatever is 5%.
Suppose that if you do have that illness, then the chance of that test detecting that you have it is 95%.
That sounds pretty good, doesn’t it?
Suppose the chance that the same test will indicate you have that illness, if you actually don’t, is just 5%.
That sounds pretty good too.
Fairly straightforward statistical analysis will show, irrefutably, that if that apparently reliable test indicates you have that illness, the chance that you actually do have it is only 50%.
Scary. But it’s true.
Suppose the chance of anyone having that illness is actually much lower, say 1%.
Then if the test indicates you have that illness, the chance that you actually do have it is only 16% !
I learned about the above from Kerry Mengersen, whose course “Bayes for Beginners” I undertook back in 2006: http://www.statsoc.org.au/CPD16