Paul’s Perfect Prognostication
Paul the octopus must be enjoying his 15 minutes of fame for correctly predicting the outcomes of eight World Cup matches in a row. In fact, a stamp in his honor is currently available at the Shanghai World Expo. This must be a welcome relief from the death threats that followed his [ultimately accurate] prediction of Spain over Germany.
Assuming that the outcome of every match was equally likely (what if you don’t?), then Paul had a 1/256 chance ( that is, (1/2)^8 ) of nailing all eight predictions. That’s roughly a .4% chance, on the order of getting dealt a straight in a five-card poker hand, or rolling a six three times in a row on a fair die. Or, if you prefer, exactly equal to the likelihood of flipping a coin and getting Tails (Arms?) eight times in a row.
Apparently octopi have short lifespans, so it doesn’t look like Paul will be around in 2014 to put his record on the line. At least he’ll go out on top.