This week's column by The Numbers Guy in the Wall Street Journal focuses on improbable events. Several events that seem intrinsically unlikely have happened in recent weeks: two nuclear submarines collided in the vastness of the oceans; two satellites collided in the vastness of space; and the two engines of a 737 airliner were disabled simultaneously by birdstrike. This last one is probably the least surprising of the three: there are several thousand birstrikes on civil aircraft every year, some of which lead to engine failure. Given that birds travel in flocks, it's not too surprising that two engine failures might happen simultaneously (these are hardly independent events!).
... Events that seem unlikely at first glance may not be that unlikely given enough opportunity. For example, Utts says, if everyone dreamed about a plane crash once in their lives, a few thousand people would have the crash dream on any given night — including the night of a crash. “These specific incidences may be unlikely, but the combined probability of something similar at some point in time is probably fairly high.”
“Everything we see has about a zero probability,” Westfall said. “Calculating these probabilities after the fact is kind of meaningless.”