If the probability of observing a car (read: at least one car) in 20 minutes on a highway is 609/625, what is the probability of observing a car (read: at least one) in 5 minutes (assuming constant default probability)?

(In reply to re(2): Auto-suggestion by ThoughtProvoker)

The solution to the problem as stated (i.e., at least one car within a specified time interval) depends on assuming independence of all subintervals within the larger interval.  As the number of subintervals becomes larger, with smaller and smaller subintervals, the original 20-minute probability (or the 5-minute probability encountered along the way) becomes the sum of many small probabilities--the limiting case being the Poisson distribution.

Admittedly both independence and the infinite splitting of intervals will fail in the real world, but the assumption in the problem is that intervals can indeed be split into independent subintervals.  Once that's true regardless of the size of the previous level of subinterval, the limiting case, the Poisson, becomes the distribution.

Posted by Charlie on 2004-04-09 14:50:43