Tuesday, December 14, 2010

Red Light, Green Light

My daily commute involves driving through twelve intersections with traffic lights.  This morning, eleven (yes, eleven) were red.  I got to thinking what the odds of that were (as I tend to do).

For most of my commute, I am on the "main road" of any intersection.  There are only two such crossings where the roads are of equal size and traffic volume.  Since each of those has a turn arrow, I will assume that they are only green for people going in my direction about 40% of the time.  Of the remaining ten lights, only one has a turn arrow unaccompanied by a green in my direction.  For that, I will assume that it is green my way 50% of the time.  The final nine lights, I will estimate are green 55% of the time.

Since I hit a green with one of the lights in the last category, the odds of this happening are:

= .6^2*.5*.45^8

=      302,672,257     

=    1   

= .000302672257

= .03%

It doesn't sound insanely small, but to put this number in perspective, IF someone were to work five days a week for fifty two weeks per year (no vacation days or holidays off), they would drive the commute 260 days per year.  Given that, this nearly a once in twelve year occurrence.  I'm thinking I should go to AC and bet it all on RED!


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