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Probabilities in Evolution

Interesting discussion on the mathematics of the evolutionary process……

Does Evolution Have a . . . Chance?

by Mike Riddle on May 30, 2014

In today’s culture, molecules-to-man evolution is being taught as a fact, even though it is known to “go against the odds.” But few realize the odds they are up against! And they are immense!

The Bible teaches that God is the Creator of all things (Genesis 1; {scripture “Colossians 1:16” %}; John 1:1–3; Revelation 4:11). While these passages rule out any possibility of Darwinian evolution, they do allow for variation within a created kind. But there is much opposition to what the Bible teaches. People holding to evolution would argue that random chance events, natural selection, and billions of years are sufficient to account for the universe and all life forms.

Do You Believe in “Magic”?

Most people recognize “magic” as an illusionary feat or trickery by sleight of hand. But how far are you willing to go to believe something can happen by “dumb luck” or chance? For example, if I were to roll a die and have it come up six three times in a row, would you consider that lucky? How about if I rolled six ten times in a row? Now you might suspect that I am using some trickery or that the die is weighted.

How far are we willing to go to accept something as a chance occurrence or before we recognize that it was just an illusion? We can test this by measuring our credulity factor. Credulity is the willingness to believe something on little evidence.

Measuring Our Credulity Factor against Evolution

Evolutionists state that life originated by natural processes about 3.8 billion years ago. Is there any evidence for this happening? Freeman Dyson, theoretical physicist, mathematician, and member of the U.S. National Academy of Sciences states:

Concerning the origin of life itself, the watershed between chemistry and biology, the transition between lifeless chemical activity and organized biological metabolism, there is no direct evidence at all. The crucial transition from disorder to order left behind no observable traces.2

Since the origin of life has never been observed, this is a major hurdle! We are left with the question, “Is the origin of life by naturalistic processes possible?” This can, in part, be tested by examining two areas:

  1. The success of scientists in creating life or the components of a living cell.
  2. The probability that such an event could occur.

The Structural Unit of Living Organisms—The Cell


Cells are made up of thousands of components. One of these components is protein. Proteins are large molecules made up of a chain of amino acids. In order to get a protein useful for life, the correct amino acids must be linked together in the right order. How easy is this and does it happen naturally? It turns out that this is not an easy process. There are large hurdles that evolutionary processes must overcome in order to build a biological protein.

Protein molecules contain very specific arrangements of amino acids. Even one missing or incorrect amino acid can lead to problems with the protein’s function.

Making Mathematics Painless

Before applying mathematics and probability to the origin of life, we need to consider seven parameters that will affect the formation of a single protein.

Amino Acid

First, there are over 300 different types of amino acids. However, only 20 different amino acids are used in life. This means that in order to have life, the selection process for building proteins must be very discriminating.

Second, each type of amino acid molecule comes in two shapes commonly referred to as left-handed and right-handed forms. Only left-handed amino acids are used in biological proteins; however, the natural tendency is for left- and right-handed amino acid molecules to bond indiscriminately.

Third, the various left-handed amino acids must bond in the correct order or the protein will not function properly.3

Fourth, if there was a pond of chemicals (“primordial soup”), it would have been diluted with many of the wrong types of amino acids and other chemicals available for bonding, making the proper amino acids no longer usable. This means there would have been fewer of the required amino acids used to build a biological protein.

Fifth, amino acids require an energy source for bonding.4 Raw energy from the sun needs to be captured and converted into usable energy. Where did the energy converter come from? It would require energy to build this biological machine. However, before this energy converter can capture raw energy, it needs an energy source to build it—a catch-22 situation.5

Sixth, proteins without the protection of the cell membrane would disintegrate in water (hydrolysis), disintegrate in an atmosphere containing oxygen, and disintegrate due to the ultraviolet rays of the sun if there was no oxygen present to form the protective ozone layer.6

Seventh, natural selection cannot be invoked at the pre-biotic level. The first living cell must be in place before natural selection can function.

Considering all seven of these hurdles, how probable is it that a single protein could have evolved from a pool of chemicals? Probability outcomes are measured with a value ranging from zero through one. The less likely an event will happen, the smaller the value (closer to zero). The more likely an event will occur, the larger the value (closer to one).

Let’s practice this using a coin. What are the chances of getting a heads when we flip a penny? The answer is 50 percent, or one chance in two (written 1/2). What is the chance of getting two heads in a row? Since each toss is 1/2 we can multiply each occurrence to get the final probability. This would be 1/2 x 1/2 which would equal 1/4 (or one chance in four). Now let’s use some bigger numbers.

When we flip a coin we have two possible outcomes, heads or tails. In this problem, we want to calculate the probability of getting all heads every time we flip a coin. We can use this exercise to test our credulity factor. How many heads in a row are we willing to accept as a chance occurrence? At what point would we suspect an illusion or some form of magic (trickery)?

The objective of using probabilities is to demonstrate the probability or chance of getting a certain result. On average, how many times and how often will we need to flip the coin to achieve 100 heads in a row? Over 300 million times a second for over one quadrillion years!

The chances of getting all heads 100 times in a row is similar to the chance of getting 100 left-handed amino acids to form a biological protein. Proteins range in size from about 50 to over 30,000 amino acids. To get a small protein of 100 left-handed amino acids from an equal mixture of left- and right-handed amino acids, the probability would then be 1030 or 1 followed by 30 zeros (1,000,000,000,000,000,000,000,000,000,000). How believable (credulity factor) is it that this could happen by random chance? Also, consider that this has never been observed! Chance protein formation has always been accepted as a matter of faith by evolutionists.

Number of desired heads in a row Probability Number of flips Credulity factor (chance)
1 1/2 have 2 Yes / No
2 1/4 (1/22) 4 Yes / No
3 1/8 (1/23) 8 Yes / No
4 1/16 (1/24) 16 Yes / No
5 1/32 (1/25) 32 Yes / No
8 1/256 (1/28) 256 Yes / No
10 1/1024 (1/210) 1024 Yes / No
20 1/1,048,576 (1/220) 1,048,576 Yes / No
100 1/1030 (1/2100) 1 followed by 30 zeros Yes / No

But wait, there is more! This number, 1030, only measures the possibility of getting all left-handed amino acids. It does not say anything about their order. In our example, we have a chain of 100 amino acids. Each position can be occupied by any 1 of 20 different amino acids common to living things, and these must be in a specific order to form a functional protein. What is the probability that the correct amino acid will be placed in position number 1 of the chain? It will be 1/20. What is the probability that the first two positions will be correct? This can be calculated by multiplying the two probabilities together (1/20 x 1/20 = 1/202). Therefore, the probability of getting all 100 amino acids in the correct position would be 1/20 multiplied by itself 100 times or 1/20100 (this equates to 1/10130). This is 1 followed by 130 zeros!


Large numbers can be hard to visualize or even comprehend. To put this in picture format we can use a smaller number 1021 (1 followed by 21 zeros). If we were to take 1021 silver dollars and lay them on the face of the earth; they would cover the entire land surface to a depth of 120 feet.7

Are there upper limits for which we can logically expect an event will not occur by random chance? The mathematician Emile Borel proposed 1/1050 as a universal probability bound. This means that any specified event beyond this value would be improbable and could not be attributed to chance.8

As we can see, the probability of getting a single small protein (1/10130) far exceeds this limit. Even if the protein can interchange amino acids at various positions (such as in the case of the protein cytochrome a),9 the resulting probability still exceeds the limit of 1/1050. So far we have only looked at the probability of getting a single small protein by random chance. What are the chances of getting all the proteins necessary for life?

No matter how large the environment one considers, life cannot have had a random beginning . . . there are about two thousand enzymes, and the chance of obtaining them all in a random trial is only one part in (1020)2000 = 1040,000, an outrageously small probability that could not be faced even if the whole universe consisted of organic soup.10

This number is so large (1 followed by 40,000 zeros) that it staggers the imagination how life could have evolved by natural, random processes. Yet, people continue to hold onto their belief that life did evolve by random chance (high credulity factor).

Time is in fact the hero of the plot. . . . What we regard as impossible on the basis of human experience is meaningless here. Given so much time, the “impossible” becomes possible, the possible probable, and the probable virtually certain. One has only to wait: time itself performs the miracles.11


This statement attributes supernatural qualities to time! It also allows for anything to happen. This means we are no longer bound by the laws of science or any other natural limits. The statement thus becomes meaningless.

Tricks of the Trade

Since scientists have been unable to create life, they are forced to speculate through research and sometimes “sleight of hand” how it might have arrived on earth. Below are some of the tricks of the trade used to avoid the obvious—that God is the Creator of all things (Colossians 1:16).

1. It happens naturally

“The formation of biological polymers from monomers is a function of the laws of chemistry and biochemistry, and these are decidedly not random.”12


This is an incorrect statement. If it happens naturally, then why can’t scientists duplicate this in the lab? Amino acids do not spontaneously bond together to make proteins. First, it takes a source of energy to do this. Second, the natural tendency is to bond left- and right-handed amino acids, but life requires all left-handed amino acids. Third, they must be in the correct order or the protein will not function properly. Fourth, it requires the instructions of DNA to get the right amino acids. Where did DNA come from? Fifth, protein molecules tend to break down in the presence of oxygen or water.

2. The deck of 52 cards

In a deck of 52 playing cards there are almost 1068 possible orderings of the cards. If we shuffle the deck we can conclude that the possible ordering of the cards having occurred in the order we got is 1 chance in 1068. This is certainly highly improbable, but we did come up with this exact order of cards. Therefore, no matter how low the probability, events can still occur and evolution is not mathematically impossible.


In this example the math is correct but the interpretation is wrong. If the arrangement had been specified beforehand, then the actual outcome would be surprising. By shuffling the cards, the probability is one that a sequence will occur. The fallacy is that the order is predicted after the fact.

3. All the people

We are in a room of 100 people. What is the probability that all 100 people would be here in this room at this exact time? The probability is enormous, but yet we are all here.


Two things are wrong with this reasoning. First, the people were not pre-specified. This is another example of an after-the-fact prediction. Second, each person made a decision to attend; therefore, this is not a chance gathering. This turns out to be a misunderstanding between a chance event and intelligent choice.

4. Probability is not involved

Probability has nothing to do with evolution because evolution has no goal or objective.


This statement disagrees with modern biology textbooks.

When there is more than one possible outcome and the outcome is not predetermined, probability can become a factor. In the case of evolution there is no pre-assigned chemical arrangement of amino acids to form a protein. Therefore, the formation of a biological protein is based on random chance. Scientists know today that it is only because of the instructions (information) in DNA that only left-handed amino acids are linked in the proper order.

Cells link amino acids together into proteins, but only according to instructions encoded in DNA and carried in RNA.13

Both creationists and evolutionists agree that DNA is essential for linking the correct amino acids in a chain to form a protein. The unanswered question is, “Where and how did DNA acquire the enormous amount of information (instructions) to form a protein?” There is no known natural explanation that can adequately explain the origin of life, or even a single protein. The evolutionists are then left to rely on the odds (chance) that such a tremendous, improbable event occurred. Molecular biologist Michel Denton puts the event in perspective:

Is it really credible that random processes could have constructed a reality, the smallest element of which—a functional protein or gene—is complex beyond our own creative capacities, a reality which is the very antithesis of chance, which excels in every sense anything produced by the intelligence of man?14

But wait, there is still more!

The Human Body, Time, and Evolution

It is estimated that the human body is made up of 60 trillion cells (60,000,000,000,000).15 How long would it take to just assemble this many cells, one at a time and in no particular order at the rate of:

One per second 1.9 million years
One per minute 114 million years
One per hour 6.8 billion years

These ages assume no mistakes! However, the evolutionary mechanism is based upon random errors (mistakes) in the DNA. Also included in assembling all the 60 trillion cells is that they have to make the right organs which all have to interact.

The human body contains more than 40 billion capillaries extending over 25,000 miles, a heart that pumps over 100,000 times a day, red blood cells that transport oxygen to tissues, white blood cells that rush to identify enemy agents in the body and mark them for destruction, eyes and ears that are more complex than any man-made machine, a brain that contains over 100 trillion interconnections, plus many other parts such as the nervous system, skeleton, liver, lungs, skin, stomach, and kidneys.

The complexity and dimensions of the human body are staggering. The probability of assembling 60 trillion cells that form specific organs that all work together to form a single human being in the evolutionary time scale of 3.8 billion years is a giant leap of faith. However, an all-knowing, all-powerful Creator has told us in His Word that He is the designer.

The hearing ear and the seeing eye, The Lord has made them both (Proverbs 20:12).

Every human body is a testimony to a purposeful Creator. As Malcolm Muggeridge said:

One of the peculiar sins of the twentieth century which we’ve developed to a very high level is the sin of credulity. It has been said that when human beings stop believing in God they believe in nothing. The truth is much worse: they believe in anything.16


Probability arguments can present a strong argument for the existence of a Creator God.


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