Home > Statistic of the Week > Archive List > Detail

<< Prev 2/26/2006 Next >>

The Key Fits, Mr. Mason

Fact 1:The New York Times (March 4, 1996) reported a case of mistaken identity, when the keys to one person's car opened the door of a second person's vehicle.

Fact 2: Both cars were General Motors vehicles.

Expert Witness Statement: The odds of a single key matching locks on two different car locks is 26,000 to 1.

Question 1: Is this statement by the expert witness reasonable? Some facts to consider or data to obtain:

  • How many cars are produced by General Motors in a single year?
  • How many different key formats are possible (is it even a finite number)?
  • Does Genral Motors purposely distribute cars with congruent keys to diverse geographical areas...or?
  • How did the witness get the number 26000?
Question 2:Try an experiment....check with your local General Motors dealer and local owners of General Morors vehicles...can you find any keys locally (i.e. in a very small finite subset) that match?

Source: Edwin Rosenberg's "Some Odd Odds," Mathematics Teacher, December 1996.