All that verbiage to get most of my explanation wrong!! LOL!
That sum (probability) that approached 1 was was actually the
probability of finding the pebble at least once in 15 tries.
Darn. At least I answered the questions ASKED correctly... how to play
to win, and what the odds are for each turn.
The calculation to get the actual probability of getting 9 (or more)
out of 15 is a little more involved, done formally, I THINK. At this
point I'm pooped and have other things to do, maybe I'll do it over the
weekend since I have to study for Math 122 midterm on Tuesday anyway.
:-)
Jim
On 5-Nov-04, at 7:33 PM, Jim Roepcke wrote:
> S, the sum of the infinite series, represents the probability of
> winning this game. A probability of 1 means you always win. Now of
> course, we're not playing an infinite amount of turns, only 15. But if
> you actually went to the trouble of calculating out the sum of that
> ugly sequence of 15 probabilities, you'd get a number very very very
> close to 1.
