Suppose you and a bunch of friends are sitting around a table.
There are N of you.
You have a jug of beer in front of you, which no one has yet tasted.
So you take a swig of it, and then pass it to your left or right with probability 1/2.
Now suppose your neighbor does the same---he/she takes a swig of it and passes it to his/her left or right with probablity 1/2.
Each player continues in this fashion.
Because the beer is moving back and forth randomly around the table, it may be a while before some people get to taste the beer for the first time.
Which person around the table is most likely to be the last one to try the beer?
Is it a person near you or far from you?
(Assume that the jug is bottomless, and never runs out.)
Source: Math fun facts
(In reply to re: computer solution
by Ady TZIDON)
I see a convincing proof that your analysis is correct, at http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-spring-2005/lecture-notes/l23_prob_randwak.pdf.
The problem with the random number generation is probably more subtle than prevalence of either +1 or -1, but rather in a lack of independence. I'll have to check further.
Posted by Charlie
on 2013-04-10 12:26:20