Regarding my earlier answer to the question, two people have written me and 
said that I misread the question. That's entirely possible:

> This assumes the smaller circle is defined within the bigger.  If the 
> question concerns *any* smaller circle within the bigger one, then the 
first 
> seed could fall anywhere.

Probabilities are always calculated on the basis of what specifies success or 
failure. I was presuming that the smaller circle was pre-specified, lying 
somewhere within the larger one. If that were the case, my previous answer 
would 
be correct.

However the way that others are reading the question is that the first seed 
specifies the center the smaller circle, essentially the same if the question 
were more along the lines of "what's the probability of getting a duplicate?" 
In that case, the first draw species what a duplicate would be. In this 
alternate interpretation, the drop of the first seed doesn't count. Rather, its 
position will be used to specify the center of the circle. If that is the case, 
then the probability of getting the next two seeds within that first 
seed-specified circle is 1/4 * 1/4 = 0.0625.

However, I am still a little reluctant to endorse that interpretation simply 
because the original question asked: "What is the probability that all three 
will be clustered within a circle of one-half meter radius?" It's the "all 
three" part of the question that gives me pause.

Wirt Atmar

Reply via email to