Three athletes with roots in the Methow Valley are on the U.S. Olympic team for the 2014 Sochi Olympics,:the brother and sister duo of Sadie and Erik Bjornsen, and Brian Gregg, who grew up in the valley but now resides in Minnesota. What are the odds?
There 230 members of the U.S. Olympic team. The population of the United States is about 310 million. So the odds of a single person selected at random from the U.S. being a 2014 U.S. Olympic athlete is 230/310000000 or about one in every one and a half million people. Call this probability p.
There are about 5000 people in the Methow Valley. Then the probability of there being exactly one U.S. Olympic athlete in the Methow Valley is 5000*p*(1-p)^4999 or about 0.0037. One in 270 ish, not that crazy.
The probability of there being exactly two U.S. Olympic athletes in the Methow Valley is 5000*4999*p^2*(1-p)^4998 or about 0.000014. One in about 730000. Nearly the same odds as a dealt royal straight flush in five card poker.
The probability of there being exactly three U.S. Olympic athletes in the Methow Valley is 5000*4999*4998*p^3(1-p)^4997 or about 0.00000005 or one in twenty million. This is just less than the odds of winning a lottery where you have to correctly choose 6 numbers between 1 and 49. Congrats Methow Valley on winning the U.S. Olympic lottery 🙂