Probabability of being caught by police? Ok, well first let me say this is a fair question but I am not encouraging anyone to test it out. Its just for fun.
In Ireland we have to get our car road tested, taxed, and of course insured. If I decided to drive my car without tax or insurance, the police could stop me and take the car away and also issue me with a big fine.
If I knew there were approximately X number of police in my area, across 3 eight hour shifts. And that they do Y number of car checkpoints (where they stop on the road and check cars passing for tax, insurance and dui) during each shift. And if I also knew that there are approximately Z number of cars in my area.
Then given a specified timeframe and a specfied average amount of driving time within that time frame. For example, over 1 year period, I might drive on average 2 hours per day. And the average in my area would be around 3 hours per day (inclusive of commercial traffic). Effectively I drive less than average. (or more depending on the numbers)
How can I work out the chances of being stopped by the police at a checkpoint? :->
Also, if you have answered the above successfully. Now show me that if I knew the approximate times and locations of such checkpoints, so they could be almost avoided. Of course my information will only be right a given percentage of the time (lets say 75%).
Now how can I work out my chances of being stopped by the police at a checkpoint? :->
Cheers!
 A: The basic number you need is the chance per hour of driving that you will be checked.  The number of cars and police don't matter.  Maybe you can approximate that there is one checkpoint per 2000 km of major highway and none off the major highways.  Then there is a sure way not to get checked-stay off the major highways.  If you drive 100 km/day on major highways and the checkpoints are random, you have about 0.05 chance per day to get checked.  It is actually a little lower.  I just made up the numbers on the fly, and this sounds much too high-you can supply your own.  Then the chance of going a year without getting checked would be $0.95^{365}\approx 7.4E-9$, pretty poor.
Added:  you can measure the chances if you want.  Get your friends to record km driven and number of stops over 1 or 6 months.  You are assuming that the roads they travel are as likely to have a checkpoint as the ones you travel.  Maybe the police find it easier to set up right in front of the station and one friend drives by on the commute to work-he will probably get checked more often.  After a reasonable time, you will have a figure for average km between stops.
