Today's question comes from my buddy Karen at the University of Michigan:
What are the odds of an individual being killed in an auto accident in Michigan (~680 deaths in 2014 so far) vs. ANY individual in MI contracting Ebola?
|Not sure if ebola or modern art. Possibly both. (Image from Wikipedia)|
At present, there are no reported cases of Ebola in Michigan. The only way to contract the disease is through direct contact with the bodily fluids of someone who already has the disease. For this reason, the only way of infecting someone in Michigan is by bringing an infected person to Michigan. Roughly 2.8 million people fly internationally into Detroit Metropolitan Airport each year.1 That's out of a total of 800 million passengers flying to or from the United States.2 According to the news, no more than 10 people have gotten on a plane with Ebola in their system. From these numbers, we can compute
probability of a random person on a plane having Ebola = 0.00000125%
probability of that plane flying to Detroit = 0.35%
This means the probability of someone with Ebola making it to Michigan is 0.0000000044%. Even if we assume the probability of contracting the disease when exposed is 100%, that's still a minuscule probability. You're about 2 million times more likely to die in a car crash in Ann Arbor than you are to catch Ebola. Thanks for a great question, Karen!
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Aaron Santos is a physicist and author of the books How Many Licks? Or How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions. Follow him on Twitter at @aarontsantos.
***Update*** After reading this post, a friend of mine commented on the inaccuracy of using data from relatively new phenomena to make predictions. In his words, "using prior cases over a few months for an event without precedent is bad modeling." I agree wholeheartedly. The exact numbers should be taken with a grain of salt. Statistics like the "likelihood of someone getting on a plane with Ebola" are clearly complex, time-dependent phenomena and need more than just an order of magnitude estimate to make useful predictions. In a more professional setting, I would model it as such. However, that's not really the point of this blog. My main goal is to get people interested in working out the numbers on their own, and using very complex models would quickly alienate readers who might already be math-phobic. If the blog inspires these people to learn more about math, and they eventually realize I'm pulling some numbers out of my ass, my mission will complete. However, even for the math-phobic, my description could have been more precise. In my friend's words,
It is better to say:
"Contracting Ebola is non-quantifiably improbable and if you're living anywhere in the developed world, you, as an individual, have bigger problems.
On the other hand, West Africans could use your government's directed attention. Perhaps you should be focusing your attention and advocacy on Ebola in West Africa because it is both morally good and in your enlightened self-interest. "
I couldn't have put better myself.