http://www.johndcook.com/blog/2009/06/25/probability-approximation/ The blog of John D. Cook Sat, 11 Feb 2012 01:10:06 -0500 http://wordpress.org/?v=2.8.4 hourly 1 http://www.johndcook.com/blog/2009/06/25/probability-approximation/comment-page-1/#comment-19969 teknas Thu, 25 Jun 2009 23:01:34 +0000 http://www.johndcook.com/blog/?p=2545#comment-19969 The birthday paradox is a more interesting variant of the problem you introduce. Here you end up picking a pair of people in a room at random and calculate the probability of finding at least a pair of them who share their birthday. Turns out with 23 people you have 0.5 probability of a pair of them sharing their birthday. Not very intuitive but the math is simple and very insightful. The birthday paradox is a more interesting variant of the problem you introduce. Here you end up picking a pair of people in a room at random and calculate the probability of finding at least a pair of them who share their birthday. Turns out with 23 people you have 0.5 probability of a pair of them sharing their birthday. Not very intuitive but the math is simple and very insightful.

]]> http://www.johndcook.com/blog/2009/06/25/probability-approximation/comment-page-1/#comment-19967 John Thu, 25 Jun 2009 22:33:13 +0000 http://www.johndcook.com/blog/?p=2545#comment-19967 Good point. Assuming independence in weather reports is unrealistic. Birthdays, sure: independence seems justified, unless you run into twins walking together. :-) Good point. Assuming independence in weather reports is unrealistic. Birthdays, sure: independence seems justified, unless you run into twins walking together.

]]> http://www.johndcook.com/blog/2009/06/25/probability-approximation/comment-page-1/#comment-19965 Danny Tarlow Thu, 25 Jun 2009 22:27:11 +0000 http://www.johndcook.com/blog/?p=2545#comment-19965 I guess it's somewhat off-topic, but the thing that always bothers me about using the probability of rain in a given day as an example is the implicit assumption that rain on each day is an independent event. In reality most times, it's more like there's a 40% chance a storm will take a certain path through the region, and if the storm does take this path, there's a near certain chance that it will rain for three days straight. I guess it’s somewhat off-topic, but the thing that always bothers me about using the probability of rain in a given day as an example is the implicit assumption that rain on each day is an independent event. In reality most times, it’s more like there’s a 40% chance a storm will take a certain path through the region, and if the storm does take this path, there’s a near certain chance that it will rain for three days straight.

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