Tom asks:
> Perhaps someone can help me with this. Iâve posed it in the form of
> an example, but it is the general question in which Iâm interested.
> Suppose three seeds fall randomly within a circle with radius of one
> meter. What is the probability that all three will be clustered within a
> circle of one-half meter radius?
If we presume that the seeds fall uniformly over the area, in the way that
rain falls onto the ground, then the probability that any one seed will fall
into the smaller area is simply the ratio of the two areas' sizes:
P(one seed) = pi * (0.5 r)^2 / pi * r^2 = 1/4
The probablility that all three seeds would fall into the smaller area is
thus:
P(all seeds) = 1/4 * 1/4 * 1/4 = 0.015625
or about 1.6%.
Wirt Atmar
