One of the favourite - and utterly brain dead - criticisms of evolution that is often raised is the "sheer improbability" of the world - and the universe we live in - having "simply occurred" as a result of highly unlikely events coinciding.
Fundamentally, this is an emotional reaction - one firmly rooted in the same insecurity that gives religion its foothold in our world in the first place. There's something very unsettling to humans about the notion that we are in many ways simply a part of nature, and not divinely privileged in any respect.
However, one has only to look as far as the complex computer systems that we have today to get some idea of how these seemingly infinitely small probabilities line up.
A number of years ago, I was tasked with finding a bug in a piece of software I was responsible for at work. Every so often a handful of projects would pop up with exactly the same fault occurring, but we could never reproduce it in our test lab.
Eventually, we did track the fault down to a single line of code that had a small, but significant coding error. However, the coding error was not likely to cause a serious problem unless the following combination of failures happened to coincide:
1. The faulty line of code executed and produced a fail condition.
2. The program received a 'page' of memory that just happened to have a meaningful value in the correct location from the last execution of the loop
3. The correct sequence of related programs executed, and left the system in a state where 1 and 2 could in fact occur and coincide.
When we found the error, one of the team spent a few hours working out what the likely combination of events was that was necessary to coincide for this result to occur - and the number was surprisingly close to 1 in a million - quite literally. When we sat down and ran the numbers, the average time between errors happened to be awfully close to when the millionth execution of that could would likely have taken place on that system.
With the exception of the code error, the rest of the events that had to coincide were quite beyond our control - effectively random for all intents and purposes. While one might argue that the computer system itself was the result of intelligent design, that misses the point. The systems in question were never designed to produce the result that was observed. The second point is that the various aspects of the computer environment were acting as independent, but interacting, systems - not unlike those we see in the world around us (admittedly the computer software involved exists on a far smaller scale than the world we live in).
So, if one were to draw out the analogy a bit further - especially when considering the fundamental concept of evolution - we find ourselves examining the probability that random biological events would be occurring, some more successful than others at propogating themselves. So, let's consider that any particular biological event (e.g. DNA mutation) has a probability of 1 / 1 x 10^7 of occurring (my estimate of the probability here is arbitrary). Now consider how many biological events occur in the world every second of every day. Cells split and reproduce all the time - think about the number of cells in our world - even in one body - the numbers are unimaginably huge, far more than 1 x 10^7 - which means that the odds are that somewhere, any one arbitrary event has occurred.
Now, thinking beyond that, then the question is whether that event occurs in a context which makes it significant? Well, if the event itself can occur, and has a pretty reasonable chance of occurring, then it is hardly an unreasonable assertion that the events could occur in the correct context to become significant.
Is this guaranteed? No. Is it impossible? No - which is by far the more significant point.
Does this preclude the existence of some metaphysical being and their involvement in our universe? No - of course not. By definition the metaphysical being is unprovable until we ourselves become peers to that being somehow.
However, it does provide us with a knowable explanation that does not require the intervention of an unknown and unprovable entity. This produces a logically consistent explanation - one which stands to scrutiny.
For some, what I postulate here is going to be emotionally unsatisfying - but that's not surprising - statistics and the mathematics of probabilities are seldom emotionally satisfying. Science in general isn't about sating someone's emotional needs.