You've tested positive for cancer! How worried should you be?
 

This is a reasonably simple mathematical problem, with a very startling result.

The premise is this:
We have a test for cancer that is 98% accurate. That is, that 98% of the subjects who do have cancer will test positive, and 98% of the subjects who do not have cancer will test negative.
You've undergone the test, and the results have come back.
Bad news! You've tested positive!
But the question is, how worried should you be?
Given that 0.5% of the population has cancer, what is the probability that you have cancer, having recieved a positive result?

(Hint: If you don't know where to begin, apply the values to a set population of say 10,000 and work from that)

Where did you get the statistic <i>"Given that 0.5% of the population has cancer. . . "</i>?

That seems rather low (by about a factor of 60), considering that cancer is the 2nd-leading cause of death in the United States (I can't speak for the statistics in Ireland)

Sorry....I didn't mean that to be a statement of fact! Yeah, you're right it does look like I meant it that way!
The 0.5% is just a part of the problem.

To make it more realistic, rather than testing for cancer as a whole, make it a test of some particular form of cancer, which 0.5% of the population have.

Well, in that case, with a population of 10,000 - only 50 people would have <i>that</i> cancer, of which 49 would test positive.

Of the remaining 9,950 people who do not have cancer, there will be 9,751 who test negative, and 199 with false-positive results.

Therefore, of the 248 people who tested positive, only 49 of them really have cancer. So - roughly - only 1 in 5 positive results are actually correct. So there's an 80% chance you don't have cancer.

And, of course, there's one poor guy out there falsely believing he doesn't have cancer.
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Added later: Of course, this assumes <i>everyone</i> gets tested for cancer - in the real world, you wouldn't be tested for it unless you were showing some symptoms, or had abnormal test results.

Wow, you're really hard to please!