Thursday, April 20, 2006

Cycling Probability Question

This post is something that I have long been contemplating but only recently have come to a mathematical conclusion on. My problem is that I am not sure what the formula is for this conclusion. So if anyone can create a formula for these results I would love to see it.

Here is the basic question:

Three people leave their homes around the same time of day. Each person lives within 50 miles of the other person and they do not know each other. They set off on their daily journey all heading in a random directions. What is the probability that they will cross the other's path at the exact same moment? Most likely almost zero.

Now change one fact. One of the three people is me on my bike. Now what is the probability that the two other people in a car will meet me on the road at the same time going in opposite directions of each other? Mostly likely high.

Now what is the probability that these other two will pass me and each other while cresting a hill or going around a blind corner? 99.9%

If only cars were not allowed on the road while I was out riding...

2 comments:

Ben-in-UK said...

well, my knowledge of roads in the south is not stellear, but since there's only like one, and it's dirt, the odds would be nearly 100%. Factor in the "Rob factor-Rf" (where the probability of falling off the bike before the hill is somewhat substansive-45% or so), however, could potentially drop those odds significantly. The function would look something like this.

Pe{x} = [p(C1) * p(C2) * R(Rp-Rf)] - Rfk

where:

Pe[x] is the probability of the event,
p(C1) is prob. of first car
p(C2) is prob. of sedond car
R is Rob (which is a function of Rob's probability minus the constant Rob factor)
Rfk is the Rob constant multiplied by k which is a measure of all of the strange shit that generally happens when Rob gets on a bike

hope that helps.

Rob said...

It is all suddenly clear to me now. I think the role of FNG has been taken by a new guy on my team. He's succesfully crashed in 2 of 5 crits this year. His big thrill this weekend was his inability to crash. He even had no less than 4 guys in the field tell him he was sketchy and that he should get himself dropped.