On December 29th, there were five bank robberies in New York City. The NPR bit on it contained this tidbit:

Anahad O'Connor, metro and breaking-news reporter for

The New York Times, says the news wasa little surrealbecause last year there was fewer than one bank robbery a day in the city.

**( So, how surreal is it, actually?Collapse )**

Under these minimizing assumptions, the number of NYC bank robberies on a given day is a Poisson distributed random variable with λ = ^{280}/_{362}. Thus, the probability of five robberies in a given day is a bit over 1 in 1000. [ λ^{5}e^{-&lambda}/5! ~=~ 0.0010645 ] That's a bit more than once every three years. That's just not surreal.

And, it's way less surreal than all of that. The same New York Times article says that bank robberies were up 54% at that point in 2008. There were 431 bank robberies in the first 362 days of 2008. Using 431 in place of 280 in the above calculations brings the probability up to almost 6 in 1000 (0.0059982). That's twice a year, on average.

The moral: probability and gut instinct are not close allies.

**( But, 2008 was almost definitely not a fluke...Collapse )**