Imagine an American visiting England for the first time who takes a bus to an interesting part of the countryside and decides to hire a car, the better to sightsee. He sets out along an empty two-lane highway, and after ten minutes of driving rounds a bend only to find a car coming the other way <i>in his lane</i>, within two seconds of a collision! Predict the outcome.
Prediction 1. Since he's been in that lane for 600 seconds, the probability he will remain in the lane for the next two seconds is (n+1)/(n+2) = 301/302 where n = 600/2. Hence the probability of collision is 99.7%.
Prediction 2. Since he's a defensive driver with excellent reflexes he waits one second to see if the other driver is going to get out of his way, then swerves out of the way of this madman. Probability of collision: less than 50%, unless the other driver has equally good reflexes.
(This actually happened to me in 1975 on a country road in Massachusetts shortly after returning from a three-month trip to Scotland. Fortunately I had the second outcome, but thinking about it even today sets my teeth on edge. The "madman" and I stared at each other for a while until I realized my mistake. A <i>really</i> good thing his reflexes were a lot slower than mine.)
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