## Friday, September 16, 2011

### Three Darts in One Hemisphere

You throw three darts onto the surface of a globe, each from a randomly chosen direction. What is the probability that all three darts are in one hemisphere?

1. 100% on the upper hemisphere

2. 1/3?

3. The probability is 1. You can draw a circle through any three points in space, and since any section of a sphere leaves a circular cut the circle through three darts must lie on the surface of the sphere. Since this circle could not be bigger than a great circle, they must lie in a single hemisphere.

4. Confused? What is the answer?

5. Aidan and Anonymous have it right. The probability is 1 that all three darts are in one hemisphere.

For a longer explanation than what Aidan gives, you can check out this elementary probability book: http://portal.tpu.ru/SHARED/k/KITAEVA/statistics/book/Tab2/ElementaryProbabilityDavidStirzaker.pdf
Just search through the document for the keyword sphere. Then you'll have to read over the chapter.

Warning, it's not that elementary to figure out the math!

Leave your answer or, if you want to post a question of your own, send me an e-mail. Look in the about section to find my e-mail address. If it's new, I'll post it soon.

Please don't leave spam or 'Awesome blog, come visit mine' messages. I'll delete them soon after.

Enter your Email and join hundreds of others who get their Question of the Day sent right to their mailbox