In a magazine recently there was a discussion about probability.
The author asserted that the probability of the event in question was approximately
(1 - 10-21)1025
How small is this number?
(In reply to
First thoughts (spoiler) -- Could be wrong by Steve Herman)
Basic limit (1-1/n)^n -> 1/e is right, but it generalizes to (1-x/n)^n -> exp(-x).
It is more convincing, however, to take the natural logarithm, as then
you can use the series log(1-x) = -x -(x^2)/2 -(x^3)/3 - ... which
shows that log(1-10^(-21)) is really very close to -(10^(-21)) so that
the log sought is close to -(10^4). Thus, the number is close to
exp(-(10^4)) which is about 10^(-4343) -- indeed small.
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Posted by Richard
on 2006-08-09 13:01:30 |
re: First thoughts (spoiler) -- Could be wrong
