In a message dated 7/11/01 6:32:14 AM Eastern Daylight Time, [EMAIL PROTECTED]
writes:
<<
That's the biggest trouble with statistics. If chances for some kind of
damage
are just low enough it all sounds just fine untill it hits you personally.
Like
a 1 in 2000 chance for spina bifida doesn't sound like too much. But so does
a 1
in a 100million chance to win the lottery. Then again neither the one nor the
other has kept people from taking those chances for better or for worse. :o/
>>
One of the most difficult notions to accept about statistics is the
inevitability of rare events if the sample is large enough. If the risk of
cancer of a specific type is 1 in 10,000 then one should expect and not be
surprised if 100 people out of 1,000,000 get this cancer (if more or less got
the disease then the statistic would change). Now this seems obvious but we
humans are good at estimating risk. 1 in 10,000 translates into "never" using
intuitive reasoning but this is wrong. As per your lottery example, the
chance of winning is essentially nil but the chance of there being a winner
is essentially 100% (sort of like the old Myron Cohen punchline -"Everyone's
got to be someplace"). Daniel Dennet has a fine example of the how difficult
it is for individuals to think about uncommon occurences in large samples.
What is the incidence of a team winning 8 straight games in a 256 team
elimination tournament?
The incidence is 100% since the winner of the tournament must win games in
all 8 rounds. (Another trick that uses the same sort of logic although
slightly off topic {Pick any number of teams in a elimination tournament 16,
56, 1775377, etc. How many games in the tournament - answer respectively 15,
55 1775376 - How to figure it out - Each team in the tournament loses one
game except the winner who loses no games. Total loses = total games).
