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The ancient gene
Suppose there is a gene that some people have that
allows them to operate ancient, not yet discovered
machines, the so called 'ancient gene'. Obviously
it is important to know who has the gene so that
they can be properly trained on those mythical machines!
What is the probability that Heidi actually has the gene?
Genesplicer Inc has developed a simple test
for the ancient gene. It turns out that about 0.01% of the
population has the gene. Unfortunately the simple test
is not perfect and in one in 10 000 cases the test comes back
with the wrong answer.
Heidi goes to the doctor to get tested.
The test comes back positive which means that she probably
has the gene.
Hint: its much lower than you think! Assume that 10 000
people take the test, what would the outcome be on average?
How many positive test results would you expect?
This problem was listed in a paper that described how
many doctors are unable to correctly interpret results,
especially when statistics are involved. I cannot find it
again, so if you know the reference please let me know.
The original problem had no reference to a well known
Sci-Fi TV series :-)
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