Christmas Puzzle: The Grinch Bug

[Photo by theogeo.]

Christmas afternoon is a slow time at our house. How shall we while away the hours until the turkey is done? With math, of course!

Check out this puzzle from Blinkdagger.

I got extremely sick and was wondering if I got a weird virus. I heard there was this Grinch Bug going around, making you sick throughout Christmas Holiday. I decided to go to the hospital to get it checked out. The doctor told me their test measurements are 99 percent accurate (regardless if results are positive or negative). This Grinch Bug only occurs randomly in the population (assume infected people are independent and distributed evenly), around 1 in every 10,000 people. He told me not to worry.

Today I got the report. It came out positive! What are the chances I actually have the disease? Should I be worried?

This is easier than many of the Monday Math Madness puzzles (or else I made a mistake in my answer — which happens more often than I would like to admit!), so students should feel free to give it a try. You have until Monday evening to send in your solution, if you want a chance at the prize.

To review probability, check out Counting 101.

Please — no hints or answers in the comments here! ! ! ! !
[At least not until after the December 29th deadline has passed.]

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