Probabilities and Assumptions

A recent article in the New York Times noted that

[…] Driving one of the suspect Toyotas raises your chances of dying in a car crash over the next two years from .01907 percent (that’s 19 one-thousandths of 1 percent, when rounded off) to .01935 percent (also 19 one-thousandths of one percent)….  It’s not worth losing sleep over.

Intriguing analysis.   Some items to note that may alter the above math significantly:

  1. Why compute the probability over the next two years as opposed to 10 or even 20 years?  (According to Toyota, about 80% of their vehicles that are 10-20 years old are still on the road).
  2. Why compute only the probability of dying?  What about the probability of being injured which is about 10-20 times higher?  Do we want our cars to be unsafe and to add to the uncertainties of the world we live in?
  3. An unsafe vehicle does not just pose a danger to the occupants of the vehicle.  It could pose greater dangers to pedestrians and passengers in other vehicles.
  4. The NHTSA database only contains reports that were filed by pro-active complainants.  Many incidents may not have been reported; one estimate is that only 20% of incidents get reported – people may just sell a car with problems and move on.   It is also at least conceivable that there have been accidents, injuries and deaths that have been wrongly attributed to driver error when in fact the vehicle is to be blamed.
driving one of these suspect Toyotas raises your chances of dying in a car crash over the next two years from .01907 percent (that’s 19 one-thousandths of 1 percent, when rounded off) to .01935 percent (also 19 one-thousandths of one percent).
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