Friday, February 26, 2010

Fun Friday Statistics

OK, everyone's seen the E-trade commercial with the talking baby who chastizes his friend Frank for playing the lottery for his financial security and gives him the "shocked face" when he doesn't win. But the baby also poses the question about his odds as: "You realize the odds of winning are the same as being mauled by a polar bear and a regular bear in the same day?"

For some reason, this probability statement strikes me as particularly hilarious, but also one that could possibly be calculated, so I decided to give it a try, although estimates are hard to come by in this arena.

From what I could claw up on the web, there have been 3 polar bear attacks in Alaska in the last 115 years. Given the current (rough) tourist rate of 2.5 million visitors a year and extrapolating backwards, your odds of a polar bear attack (in Alaska) is roughly 0.000000012, which is small. Note that I didn't try to accurately map the tourism increase in AK over the past 115 years; I'm just roughing the calculations here.

According to some web-based Yellowstone statistic, your odds of being mauled by a grizzly (the regular bear, which leaves out blacks and browns, I know) is 1 in 1.9 million (or 0.00000053).

Thus the odds of being mauled by both - not on the same day, just in your lifetime - is the product of those two, which leads to an extremely low probability of 6.36 x 10^-15 (or 0.00000000000000636). I skipped trying to extrapolate to mauling on the same day, because I'm assuming the first mauling results in fatality, so you'd never have to face that second mauling within 24 hours.

How low is that? Well, according to several sites on the web, the total number of humans (homo sapiens) that have ever lived/been born is roughly 106 billion (106,456,367,669 if you want accuracy). You can look at these sites if you're more interested in human population history:

But the reality of it is that the total population is 1.06 x 10^11, so being mauled by a polar bear and a regular bear probably hasn't yet happened to a human being.

I nominate Dick Cheney or Henry Kissinger to be the first.


pygalgia said...

Well, that was fun.
(fixed your links).
Excuse me while I place my bets on a worm race.

Anonymous said...

I would like to point out that you made the assumption that being mauled by a polar bear and a regular bear are independent events. I would argue that the first mauling would skew the probability of the second probability, making them dependent events and thus making the math much more difficult!