Jump to content
BrainDen.com - Brain Teasers
  • 0

Probability of picking a natural digit


BMAD
 Share

Question

10 answers to this question

Recommended Posts

  • 0

Are all the natural numbers written on slips of paper and put into a hat?

 

The probability is 1.

Agree.

 

If the problem is modified to: pick a random 'n' digit number (leading zeros are permitted). What is the probability that it has a digit '1'? The answer is: (10n - 9n)/10n. Now as, 'n' tends to infinity, the ratio approaches '1'.

  • Upvote 1
Link to comment
Share on other sites

  • 0

Sure. Graham's number has so many digitis, it's a virtual certainty that it, and every greater number, contains at least one of each of the digits 0 1 2 3 4 5 6 7 8 and 0. But even though Graham's number is almost indescribably large, there are infinitely more larger natural numbers than smaller ones.

 

Therefore the probability requested in the OP is 1.

Link to comment
Share on other sites

  • 0

karthickgururaj,

bonanova is correct that the probability is so close to 1 that it is extre-e-e-e-mely improbably that you would pick a number that did not contained the digit 1 from the set of natural numbers where the upper bound was Graham's number. What isn't true is that this probability is 1. Though extremely small, the probability is not infinitesmally small which is a requirement to correctly declare it to be exactly equal to 1. I believe bonanova was just trying to make the point that it is so close to one that you would not have lived long enough, even if you were born with the Big Bang and began your count then, to count the number of 9's past the decimal point in the probability when it finally was a different digit, thus it may as well be treated as 1.

Link to comment
Share on other sites

  • 0

:thumbsup: Right! Lower bound. :thanks:

And to further clairfy for others, the probability that is "virtually certain", as bonanova just stated in the previous posts, applies to using Graham's number as the lower bound. For the set of natural numbers, the probability is so infinitesimally distant from 1, that it is 1.

Edited by DejMar
Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
 Share

  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...