Evolution vs intelligent design (part 3)

Evolutionists claim that mutation and natural selection are the driving forces for evolution. Evolution may seem to be random, but in the vast span of time (tens and hundreds of billions of years), anything could happen, so they claim.

Let's suppose they are right, and attempt to calculate how much time it needs for mutation to produce new species.

For simplicity, let's suppose there is only 100 base pairs of differences in DNA sequence between modern human and its "ancestor" ape (the differences are in fact in tens of millions of base pairs). We know there are only four different elements (A T G and C) that make up the sequence of DNA. So the probability of a single generation of mutations to "evolve" ape DNA into human is one in every 100th power of 4. That equates to one in every 1.6X10^60.

Now let's again assume a single generation of mutation takes only one hour (but in truth, a generation equates at least tens years for the apes). So for the mutations to produce human DNA sequence from Ape DNA sequence, it will take 1.8X10^54 years. The age of the universe is about 10^10 years. So in the whole history of the universe, mutation cannot even generate 100 base pair of exact DNA, let alone change an ape into human.

Moreover, nature has a mechanism of preventing mutations from occurring. Every living organism has a proof-reading mechanism for reproduction, so that a chicken will bear a chicken, and a big will bear a pig. In fact, even a single mutation may proves to be fatal. I am wondering at what point of the evolution process did this proof-reading mechanism come to being? Why is this mechanism universally present in every organism, even those considered very primitive (such as virus and bacterium).

Evolution is simply wrong!