Geneticists are able to use specific principles to explain the observations made during genetic studies. what can geneticists use the principles of probability for?

Probability is what chance something has to happen. The Punnet Square is a way how to predict in genetics how likely an offspring is to have a trait passed on from parents, or in other words find out the probability of a trait being in the phenotype or the phenotype.
Every enzymatic transaction, every diffusion event, every cellular process only has a certain probability of working. Some of them are very low, but as long as they happen sometimes it's enough for the cell to operate. Thus the cell works around the clock to maintain certain concentrations of certain substrates. 
This occurs with polymerases, the large and small components of ribosomes, even dNTP's. The cell can ensure that a process will occur even though it will likely fail 90% of the times molecules have a chance to interact as long as there are enough molecular substrates present.

Sugar + oxygen > carbon  dioxide + water + energy  c6h1206 + 6o2 > 6co2 +6h2o + energy  and the numbers after the element symbols are small.