Lets attempt a calculation of the likelihood of the formation of a single protein by random chemical reactions within a hypothesized primordial soup on the primitive Earth. For a relatively short protein of just 100 amino acids, we can calculate a separate probability in relation to each of five specific difficulties.
Combining all of these independent probabilities related to the forming of one short protein molecule by random chance processes, we estimate the overall probability as
Now, it has recently been determined that a minimal functioning cell (an obligate parasite) must have no fewer than 265 protein-coding genes (Clyde A. Hutchison III, Scott N. Peterson, Steven R. Gill, Robin T. Cline, Owen White, Claire M. Fraser, Hamilton O. Smith, J. Craig Venter. 1999 [Dec 10]. Global Transposon Mutagenesis and a Minimal Mycoplasma Genome. Science, Vol. 286, pp. 2165-2169). Assuming that each gene codes for a single protein, this implies that the cell requires at least 265 proteins to operate as a living cell. In that case, considering proteins only, the probability of a complete living cell coming into being through random, chance processes would be
If we ponder that the whole universe is estimated to consist of only about subatomic particles, that fewer than seconds have elapsed since the alleged Big Bang, and that mathematicians reckon that an event with a probability of less than is effectively impossible, the above calculation easily destroys any hope whatsoever of a random, chance chemical origin of life! (Its interesting that the noted astronomer Fred Hoyle arrived at a similar figure of through a different route [1981. Evolution from Space. New York: Touchstone. p. 24].)
Of course, many biomolecules other than proteins are required for a fully functioning cell to be able to metabolize nutrients and reproduce itself. The above calculations have considered only proteins, and have not looked at carbohydrates (needed by cells as nutrients), lipids (constituents of cell membranes), or nucleic acids (extremely complex information molecules such as DNA and RNA, found in all cells).
A further difficulty is that random chemical reactions are more likely to lead to the destruction of any partly-formed protein than to its continuing increase in size! As stated by evolutionary biologist and Nobel laureate George Wald: In the vast majority of the processes in which we are interested the point of equilibrium lies far over toward the side of dissolution. That is to say, spontaneous dissolution is much more probable, and hence proceeds much more rapidly, than spontaneous synthesis (Scientific American, Aug 1954, pp. 44, 49-50).