## Thursday, September 30, 2010

### Safety in Numbers

It’s commonly said that airplanes are the safest mode of transportation. It’s true that more people die in car crashes than plane crashes each year, but most people also drive more often than fly.  On a "per trip" basis, which mode of transportation is safer?

The question did not specify whether we were considering just crashes in the U.S. or in the entire world.  Assuming crashes are equally likely in all parts of the world, the “fatalities to trips” ratio should be about the same in both cases.  Just make sure you are consistent (i.e. don’t divide the number of U.S. plane crash victims by the total number of flights in the world.)

According to “Ask a Scientist” 1, in the U.S. there are

“…about 40,000 deaths per year in automobile accidents vs. about 200 in air transport.”

You can check these numbers against other references to make sure they are accurate.  To answer the question, we need to estimate how often a person flies and how often a person drives.  On average, we might guess that an American flies about once per year.  This is reasonable since you’d certainly expect people to fly more than once every 10 years and less than once per month.  In contrast, most of us drive (or ride in) a car about twice per day, even if it’s just to get to and from work or school.  Since there are 3.1×108 Americans, this means there are

# flights per year = (1 flight per American per year) × (3.1×108 Americans)
= 3.1×108 flights per year,

and

# car trips per year= (2×365 car trips per Amer. per year) × (3.1×108 Americans)
= 2.2×1011 car trips per year.

The fraction of deaths is then just,

Fraction = (# deaths per year) / (# trips per year)
= (200 deaths per year) / (3.1×108 plane trips per year)
6.5×10-7 deaths per trip

or

= (40,000 deaths per year) / (2.2×1011 car trips per year)
1.8×10-6 deaths per trip.

You are 2-3 times more likely to die in a car trip than a plane trip, so according to our numbers plane travel is still safer.  Given the precision of the estimation, it’s possible that other reasonable assumptions would come up with the opposite result, since both figures are within an order of magnitude of each other.

[1] You can find this stat and a nice discussion of the topic at here.  Their numbers are different partly because they’re talking about fatalities per mile not fatalities per trip.