The Probability of Life
Creationists often claim that the chances of a modern enzyme forming by random means are astronomically small, and therefore the chances of a complete bacterium (which is composed of hundreds or thousands of such enzymes & proteins) is so near to impossible that it would never happen in the 13 billion years or so since the universe took shape.
The main problem with this argument is that it assumes abiogenesis (the initial formation of life from simpler molecules) was a totally random process. It also assumes that in order for abiogenesis to be successful, a complete microbe would have had to form spontaneously. In fact, the same non-random forces which propel biological evolution also propelled abiogenesis. Specifically, Natural Selection.
The calculation which supports the creationist argument begins with the probability of a 300-molecule-long protein forming by total random chance. This would be approximately 1 chance in 10390. This number is astoundingly huge. By comparison, the number of all the atoms in the observable universe is 1080. So, if a simple protein has that unlikely chance of forming, what hope does a complete bacterium have?
If this were the theory of abiogeneisis, and if it relied entirely on random chance, then yes, it would be impossible for life to form in this way. However, this is not the case.
Abiogenesis was a long process with many small incremental steps, all governed by the non-random forces of Natural Selection and chemistry. The very first stages of abiogenesis were no more than simple self-replicating molecules, which might hardly have been called alive at all.
For example, the simplest theorized self-replicating peptide is only 32 amino acids long. The probability of it forming randomly, in sequential trials, is approximately 1 in 1040, which is much more likely than the 1 in 10390 claim creationists often cite.
Though, to be fair, 1040 is still a very large number. It would still take an incredibly large number of sequential trials before the peptide would form. But remember that in the prebiotic oceans of the early Earth, there would be billions of trials taking place simultaneously as the oceans, rich in amino acids, were continuously churned by the tidal forces of the moon and the harsh weather conditions of the Earth.
In fact, if we assume the volume of the oceans were 1024 liters, and the amino acid concentration was 10-6M (which is actually very dilute), then almost 1031 self-replicating peptides would form in under a year, let alone millions of years. So, even given the difficult chances of 1 in 1040, the first stages of abiogenesis could have started very quickly indeed.
Please note: this article uses a hypothetical self-replicating peptide as a model molecule for these calculations. The current theories of abiogenesis are usually based on the "RNA World" theory, where in fact self-replication was first acheived through RNA molecules, rather than DNA molecules.
See the references below for more information on the RNA World Theory.