The scientific concept of the origin of life on earth begins with the premise that life first appeared billions of years ago with the formation of microscopic organisms out of inanimate matter. In the billions of years which followed, small organisms evolved into higher and more complex forms of life through random mutations, and one species evolved into another.
Over the years, a process referred to as "natural selection" weeded out those mutations and organisms less fit to survive than others. Thus, it was mostly the more "fit" that passed on their genetic character traits to subsequent generations. And that's how we and all other life forms got here.
On the surface, this sounds great. However, a deeper analysis of the underlying mechanism and the fossil record, leaves little doubt that mutations of a random nature could not possible have been the driving force behind the development of life on earth.
When it comes to a random process, there is always the question of whether it can produce organization. An analogy might be the old monkey on a typewriter: given enough time, can a monkey on a typewriter produce the works of Shakespeare purely by random keystrokes? Let's assume for the purpose of this discussion that this is possible — and that random mutations, given enough time, can also eventually produce the most complex life forms.
Let's begin by rolling a die (one "dice"). To get a "3," for example, you'd have to roll the die an average of six times (there are six numbers, so to get any one of them would take an average of six rolls). Of course, you could get lucky and roll a 3 the first time. But as you keep rolling the die, you'll find that the 3 will come up on average once every six rolls.
The same holds true for any random process. You'll get a "Royal Flush" (the five highest cards, in the same suit) in a 5-card poker game on average roughly once every 650,000 hands. In other words, for every 650,00 hands of mostly meaningless arrangements of cards (and perhaps a few other poker hands), you'll get only one Royal Flush.
Multi-million dollar lotteries are also based on this concept. If the odds against winning a big jackpot are millions to one, what will usually happen is that for every game where one person wins the big jackpot with the right combination of numbers, millions of people will not win the big jackpot because they picked millions of combinations of meaningless numbers. To my knowledge, there hasn't been a multi-million dollar lottery yet where millions of people won the top prize and only a few won little or nothing. It's always the other way around. And sometimes there isn't even one big winner.