Genetics is a science but it does not give precise answers. At best it will
give you the probability of a gene being inherited by offspring. It will not
allow you to say yes this will produce an offspring for this trait unless it
is known that both parents are homozygous for that trait. Breeding is all
about probabilities and the likelihood of offspring inheriting a trait from
the parents. A basic understanding of chance and probability is important
for breeders.

If you
toss a coin a 100 times it would be no surprise if the ratio of heads to
tails were not 1:1. Whenever chance operates there is usually a difference
from the theoretical value. If you toss a coin and get 7 heads 3 tails you
would accept that but if you did it a 1000 times and got 700 heads and 300
tails you would wonder what was strange with the coin.

Likewise it is a matter of chance which sperm gets to fertilize an egg. The
resulting zygote is therefore a random sample of what might have been. The
larger any sample the more reliable the result. It is important to realize
that small samples may give unreliable results. The effect of chance becomes
less as numbers increase.

Ratios
are not the best way for horse breeders to think in terms of as many horses
will have few offspring and a ratio of 3:1 in a family of two does not make
a great deal of sense. It is more sensible to think in terms of
probabilities. Breeding is all about probabilities and trying like the
punter to move the odds in your favour. If you do not mange to move the odds
in your favour you will end up losing. The probability of an event is the
chance that it will happen. The probability of tossing a coin to land heads
up is just slightly less than ½ .The probability of an impossible event is
0.The probability of a certain event is 1. The probability of two
independent events occurring is the product of their two individual
probabilities.

So,
for example, using Mendel and his peas; the probability of a wrinkled seed
is ¼, the probability of a green seed is also ¼ and the probability of being
both green and wrinkled is therefore ¼ x ¼ = ^{1}/_{16}. The
probability of being both smooth and green is therefore ¾ x ¼ = ^{3}/_{16
}and so on.