
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 14th, 2008, 07:06 AM  #1 
Newbie Joined: May 2008 Posts: 3 Thanks: 0  Odds of seeing all possible values
Is there a way to compute the odds of seeing all possible values in a set of values? For example, on average, how many times would you have to throw a 6 sided dice to see all 6 possible numbers? Or, if you have a 1000 items in a database and you are shown one randomly, on average, how many times would you be shown items before you have seen each item at least once? For the dice problem, I simulated it in Excel and after 5000 runs I had an average of 15 rolls before you have seen all 6 possibilities. I'm just looking for the mathematics to verify this answer. 
May 14th, 2008, 08:51 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
I find an average (expected number of flips before all sides show up) of 14.7, exactly, for a sixsided die. Other averages: 3 for a fair coin, 25/3 for a threesided die, and 761/35 for an eightsided die. I'll see if I can explain my method. 
May 14th, 2008, 11:57 AM  #3 
Newbie Joined: May 2008 Posts: 3 Thanks: 0 
This is what I came up with: For the dice example N = 6 1 + 1/((N1)/N) + 1/((N2)/N) + 1/((N3)/N) ... + 1/((N5)/N) I just don't know how to express this or solve it more concisely. Using the above I would still have to do 1000 calculations if N = 1000. 
May 19th, 2008, 06:15 AM  #4 
Newbie Joined: May 2008 Posts: 3 Thanks: 0 
For anyone else that may happen upon this... This problem is more famously known as the "Coupon Collector Problem". Just do a search for that and you will find lots of information. An approximation for the solution is: N*ln(N).


Tags 
odds, values 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
What are the odds?  Ebed  Advanced Statistics  3  January 23rd, 2014 07:48 PM 
What are the odds?  Sixteen08  Advanced Statistics  1  April 25th, 2013 02:01 PM 
What Are The Odds Of This??  travelin4fun  Advanced Statistics  4  July 26th, 2012 06:05 AM 
find values of ? that correspond to the ? values?  space55  Calculus  0  October 10th, 2010 03:23 PM 
What are my odds  mbodenheimer  Number Theory  3  December 31st, 1969 04:00 PM 