"K Barrett" wrote in message .net...
Wow! I can feel the rust slowly breaking loose from my brain. Its been a
LONG time since I had to think about this stuff and thanks for taking the
time to answer me. I am guilty of confusion and oversimplification, stemming
from sloppy thinking.

If we take your's and Steve's hypothetcial and agree that your math is
correct we see that the probability that an offspring would have *no*
genetic material from a grandparent to be 0.0009765625

My question is: Isn't that probability kind of small? Or maybe my question
is: Is that a small probability? Is that what you meant by Helmut
overstating his point?

Yes, it is small. And for normal human families, it means the event
in question it is highly unlikely. However, for orchids that will
produce 100,000 seeds, it will happen an average of 98 times. But, if
you're masochistic enough to do so, you can compute the probability
that it doesn't happen for any given sample size. The procedure is
conceptually the same as computing the number of human families with
four children of the same sex, and none of the opposite sex: in every
case, the probability of a boy or a girl being conceived is 0.5, but
we also know that the sex ratio within many families is not 1:1.

The statement I said was overstated is this (quoted from the first
nore in this thread) "For these hybrid progeny it is a virtual
certainty that some
of these cultivars carry no chromosomal genetic material from a given
grandparent, or older ancestor".

There is no such thing as a virtual certainty in this context.

Any event that can be assigned a probability may happen or it may not
happen. If there is enough data available to be able to estimate a
probability of an event, we may observe the event if we watch long
enough, but even if the probability is 0.9999999999999999999999999, it
still may not happen, and if the probability is only
0.000000000000000000001, it still may happen. Only if the probability
is exactly 1.0, is it theoretically certain that the event will occur,
and even then, in practice, the likelihood is that there was
insufficient data available to be able to measure just how much less
than 1.0 it is. Similarly, only if the probability is exactly 0.0, is
it certain that the event will not occur, and even then, in practice,
the likelihood is that there was insufficient data available to
accurately measure it. It is essential to have enormous sample sizes
in order to estimate the probability of rare events, not to mention to
study them, and so it is usually outrageously expensive to get the
data required to study rare events.

Cheers,

Ted