Statistics Question(s) of the Day

#1
I saw the thread for statistical quote of the day and I thought it would be a good idea to start this one. I realize we get new questions everyday, but this thread can be used for problems that serve no purpose other than to be interesting/leisurely (if this makes any sense). I don't know how far this will go since posting questions and the solutions might become tedious. The questions can be trivial or challenging. Maybe it will become a thread for pondering. Let me know what you guys think.

Anyways, I found the following problem in Frederick Mosteller's Fifty Challenging Problems in Probability with Solutions: The Ballot Box- In an election, Henry and David have h and d votes respectively, h>d, for example 3 and 2. If ballots are randomly drawn and tallied, what is the chance that at least once after the first tally the candidates have the same number of tallies?
 
Last edited:

Dason

Ambassador to the humans
#2
I wouldn't have expected anybody that wasn't involved in the original thread to know this but we actually have had a discussion about this particular problem before: http://www.talkstats.com/showthread.php/20437-Interesting-voting-probability-puzzle?

I've given a small version of this (I think possibly the exact example you give where h=3 and d=2) as a homework assignment. In the small case it's easy enough to enumerate all the possible paths. I leave the general case as extra credit. One or two students typically take the time to either search out the solution on the internet (this is most likely what happened but either way they show interest) or solve it on their own. I think it's a fun problem and the solution can illustrate the powerfulness of a symmetry argument.
 
#3
Thanks for pointing it out. It's the thought that counts I guess. Maybe there will be other contributors. Or I can find a new problem.
 
#4
I have a new question. It's inspired by a combinatorics problem that I saw a few months ago. I made it into a probability probability problem just because it was easy to do so.

I'm thinking of a positive integer Z. I have tickets in a box labeled 1,2,3,...,Z If each ticket is equally likely to be chosen, what is the probability that I select a number that evenly divides into Z? It doesn't matter what Z is, you can derive a formula for the arbitrary case. The problem is pretty innocent, just involves some number theory.

I like this problem for one reason: Now, when a student is blindly guessing at positive divisors, I can naively say "Well, you've got about an x% chance of guessing correctly. Keep trying." This is assuming the student picks an integer between 1 and Z, which is surprisingly never a given.