Creationists often ask how we know that random mutations are responsible for the observed differences between genomes in modern species. That is a fair question, and one that also has an answer.
As it turns out, not all mutations have an equal chance of occurring. When we say that mutations are random we mean that mutations are random with respect to fitness. A good analogy is the game of Craps where the roll of the dice are random even though 7 is going to occur much more often than 2 or 12. When we say that the dice are random in the games of Craps we mean that the dice are not influenced by which result will cause you to win or lose. In the same way, the processes that produce mutations are blind to which genetic changes will increase or decrease fitness.
Continuing the Craps analogy, CpG mutations are observed to occur at a much higher rate than non-CpG mutations where CpG refers to a CG base doublet (i.e. 5'--C--phosphate--G--3' for those molecular biologists out there). Therefore, a CG is much more like to be converted to a GG than an AT will be converted to a GT. This has to do with some basic biochemistry which makes CpG's much more like to be mutated than non-CpG's. CpG's are like a 7 in craps.
When we look at the differences between human genomes these biases are readily apparent. CpG mutations are much more common than non-CPG mutations. So what about comparing the chimp and human genomes? If we see the same bias in mutations when we compare the chimp and human genomes, then this is very strong evidence that the same processes we observe changing genomes today was also responsible for the differences between the chimp and human genomes. So what does that comparison look like?
Figure 4. Genomewide average frequencies for various nucleotide differences between chimpanzees and humans (A) and among humans (B). Ti = transitions.
This is the fingerprint of random mutation. (A) represents the differences between the chimp and human genomes broken down by type of mutation, and (B) is the same info when comparing human genomes to each other. The same bias of random mutations occurring in the human genome is the same bias we see when we compare the chimp and human genomes. This, along with other evidence, is how we know that random mutations are responsible for the divergence of the human and chimp genomes.