perplexus.info :: Numbers : So how small is it then?

Home > Numbers

So how small is it then? (Posted on 2006-08-09)

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.)

Explanation for Puzzle Answer

Comment 17 of 17 |

(In reply to Puzzle Answer by K Sengupta)

E=(1 - 10^(-21))[(10^25)] (say)

Let x= 10^21

=> 10^25 = (10^4)*x

Then, we must have:

E = (1 - 1/x) ^[(10^4)*x]

= [(1 - 1/x)^x]^10,000

Now, we know that for very large x:

(1-1/x)^x ~= 1/e

Consequently, E ~= (1/e)^10000

~= 1.135*[10^(-4343)]

Posted by K Sengupta on 2022-04-19 22:56:44

Please log in:

Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info