## Crunching The .3 Doctrine

by

Jonah,

You probably have a lot of others e-mailing as well to point this out, but while that 0.3% seems like a small probability it is wholly implausible. Just as a point of comparison given what I’ve seen on the departure screens at every airport I’ve been in, there has to be at least 1000 or more domestic airline flights every single day – probably many times that number. If the probability of an accident were 0.3% that would translate into an expected 3 crashes every single day (0.003*1000)! So are we to believe that the probability of an aircraft accident is many orders of magnitude smaller than the probability of an asteroid destroying all life on the planet? Preposterous!

If you click through to the original story, you can see the trick they used to sensationalize this. The 99.7% probability applies to the asteroid passing the earth in a particular range of distances – say 10,000 miles to 30,000 miles. There must be a decidedly non-trivial probability of it passing by at an even greater distance (> 30,000 miles). I am positive that adding the 99.7% probability to the probability of it passing even further off gives something like 99.999999999999999999%. And even at that, I bet I’m short a whole lot of nines.

Update: Math Fight! From a reader:

Now I’m SURE you’re going to get a lot of e-mails.

Your latest post referring to the probability of plane crashes is comparing apples and oranges, and shows that the e-mailer is not clear on his use of probabilities (Derb can probably chime in much more eloquently than I can).

I believe the 99.7% was the probabiliy of the asteroid thing happening once within a particular time period. Your e-mailer applies that same probability to each individiual plane each day. WRONG! Probabilities are calculated much differently than that. Go ask Derb for help!!!

Update II: More number crunching here.