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So how small is it then? (Posted on 2006-08-09) Difficulty: 3 of 5
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?

See The Solution Submitted by Jer    
Rating: 4.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: This is a notation trick | Comment 13 of 17 |
(In reply to This is a notation trick by Seth)

0.9 * 0.9 = 0.81

0.99 * 0.99 = 0.9801

0.999 * 0.999 = 0.998001

If you multiply the number more times...

0.99 ^ 45 = 0.63618548606387122457727826959944

0.99 ^ 100 = 0.36603234127322950493061602657252

So if you add an insane amount of nines (this number should have about 21 9's or so), and add a larger exponent...

0.999999999999999999999999999999 ^ 45 = .999999999999999999999999999955

0.999999999999999999999999999999 ^ 200 = 0.9999999999999999999999999998

And so you can pretty much imagine the number is almost equal to 1, and therefore, extrapolating for more 9's and for a larger exponent, the probability of that event is near 100%.

I may have it wrong, but it's what I can gather from this.


  Posted by Alexis on 2006-08-22 01:19:09
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