davej@gemed (David Johnson) (10/12/89)
Yesterday, I received a 1929 nickel in my change. This prompted
the following string of thought:
What is the probability of finding a complete set of "standard"
coins for any given year (for North Americans, that would be the
penny, nickel, dime, and quarter) in your day-to-day pocket change
without any special effort?
By special effort, I mean buying rolls of coins from banks, etc.
There is obviously a time-element involved here as well; I suspect
that the probability is low if time (t) is small (i.e. 10 minutes)
and relatively high if t is large (i.e. 10 years).
This looks like an interesting back-of-the-envelope calculation to do.
I don't have an "right" answer (I do have some hunches, though).
The sheer number of variables is interesting: Number of coins minted,
number of coins destroyed, number of coins in circulation, the (American)
tendency to hoard pennies, average "flow" of change through your pocket,
and on and on.
So, I propose two problems to be solved:
1. Provide the formulation for P(y,t) where:
y - the year of interest (e.g. 1929)
t - the amount of time to allow (e.g. 6 months)
(I don't suspect anybody will tackle this one ;-) )
2. Provide a back-of-the-envelope calculation for the
value of P(your favorite year, some reasonable time limit).
To be fair/interesting, your favorite year should probably be
between 1900 and 1980. I certainly suspect that P(1989,1 month)
is 1.
Enjoy!!
--
David J. Johnson - Computer People Unlimited, Inc. @ GE Medical Systems
gemed!python!davej@crd.ge.com - OR - sun!sunbird!gemed!python!davej
"What a terrible thing it is to lose one's mind." - Dan Quayle