## Monday, September 9, 2013

### Probability WONK

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Robert Jernigan WONK Challenge from American University on Vimeo.
I finally saw my American University WONK Challenge Spot on the Jumbotron at the Washington Nationals game on August 27. Here's me pointing, and the Nationals won!
Foul balls have really hit the news lately with a fan in Cleveland catching 4 in one game this last month! As I mention in the spot some put the probability of catching a foul ball in any game at about  1 in 1000. This, of course, varies with where you sit. Defending or attacking this figure was not possible in such a short spot, so if we accept it, we compute the probability that you catch at least one foul ball in say, n, games. We can compute this probability by first finding the probability of its complement.  The complementary event of catching at least one foul ball is catching no foul balls. In one game our chance of not catching a foul ball is 1-0.001=0.999. If our catching a foul ball is independent from game to game, then our chance of not catching a foul in n games is (0.999)n. Subtracting this from one, we get the probability of catching at least one foul ball in n games: 1- (0.999)n. If we want this result to be at least 50-50 (that is, 0.50) we need to find the value of n so that: 0.50 < =1- (0.999)n. You can do this by trial and error on a calculator or by using logarithms to solve for n. This will be the number of home games you must attend to increase your chances of catching at least one foul ball to at least 50-50. Now convert this to seasons of home games. There are 162 games in a season, but only 81 are home games. You should get an answer of 8 home seasons plus about half of a ninth season, hence choice B in the video.

This was fun to do.