Jump to content
BrainDen.com - Brain Teasers
  • 0

Hurry up and Wait


bonanova
 Share

Question

A discrete event (like rolling a fair die and wanting a 3 to appear) has a probability p of success (1/6 in this case.) The first roll is likely to fail, so let's keep rolling the die until we do get a 3, Then stop and write down the number of rolls that it took. Let's repeat the experiment a large number of times, each time recording the required number of rolls. So we have a bunch of 1s (the number of times 3 appeared on the first roll,) 2s (the number of times a 3 appeared on the second roll,) and so forth.

What number will most appear most often?

Link to comment
Share on other sites

3 answers to this question

Recommended Posts

  • 0
 

First, I have strep throat, so curse you for making me think about this.  I have no logical way to prove it on paper, but it is counter-intuitive.  My initial assumption was that it was either 3 or 4.  I wanted to see which would come out more often without using brain power.  I washed my hands and started rolling dice.  After 250 times, the number of times that comes up most often is 1.  I probably should have thought that, since anything that ends the trial removes the odds for future results, and the first time always has a chance, even if it is only 1/6.  Considering the other 5/6 of the time has to be distributed to all numbers above 1, it does now make sense in my head.

Thanks, Bonanova!

Edit: And now that I've posted this, I think proving it might be pretty trivial.

Edited by Molly Mae
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...