can any math genius out there help me?

<p>Can’t help but throw in two more percents.</p>

<p>Let’s make a test very precise and see what happens.
One person in every 1000 of a population is known to have tuberculosis.
Test is 100% accurate for a person with tuberculosis.
There is a (1/9)% chance that a person with no tuberculosis will register positive.
If a person tested positive, what are the chances that s/he has tuberculosis?
</p>

<p>Should be very high, right?
My answer - 47%.
Math defeats common sense.</p>