Chance and Intelligent Design 3

By James A. Choury, serving with WorldVenture in North Brazil

[leia este artigo em Português]

To answer the query concerning the probability of the universe and life coming into being by chance we need to understand how probability is defined and calculated.

Probability: The number of possible ways of attaining a result divided by the total number of possible outcomes. Probability is always a fraction between 0 and 1.

Examples: The chances of getting a head on any toss of a coin is ½ because there is only one way of getting a head and there are two possible outcomes of tossing a single coin; heads or tails. Therefore the probability is ½ or .50 or 50%.
The chances of rolling a die and getting a one is 1/6 because there is only one way to get a one on top and there are six different ways a die can land. So the probability is 1/6 or .16666666…. or 16.66 %.
The chance of getting a four in rolling two dice is 3/36 because you can get a 1-3 or a 3-1 or a 2-2 and the total number of possible outcomes is 36. So the probability is 3/36 or 1/12 or .0833333…. or 8.33333%.

We should notice that a greater number of possible outcomes results in a smaller probability of any one of them occurring. Any outcome of tossing a single coin (only two possible outcomes) has a greater probability than any possible outcome of tossing a die (six possible outcomes). We also note that tossing two dice creates many more possible outcomes (36) and hence the probability of any particular outcome is considerably reduced. In Mathematics, this last phenomenon is termed “joint occurrence”. Joint occurrence calculations give us the probability of event A and event B both occurring by chance.

We say two or more events are independent when the outcome of any particular one has nothing to do with the outcome of the others. Tossing one coin twice or tossing two coins at the same time are examples of independent events. To calculate the probability of joint, independent events we simply multiply the probability of one by the probability of the other or others. Since probability is always a fraction between 0 and 1 we always come up with smaller and smaller probabilities as the number of joint events increases (unless we are dealing with certainties). That means that getting all heads when tossing 5 coins is much less likely than getting all heads when only tossing one coin (3.125% as opposed to 50%).

What does this have to do with evidence of God’s existence? Let’s look at some examples:

Example #1. You walk into a room. There is a table in the room and among the normal clutter there are five coins on the table. All the coins are heads up. What do you conclude? The odds of five coins being all heads up on the table is 1/32. By chance there is only one way all the coins could end up all heads. There are 31 ways that they can end up not all heads up. (They must be either all heads up or not all heads up by the law of the excluded middle). What would a reasonable, unbiased, rational person conclude when finding himself in a room with a table with five coins on it all heads up? It is possible that it just happened by chance but it is much more probable and reasonable that someone was arranging things that way. It is 31 times more probable that someone was arranging things. Suppose there are fifteen coins on the table all heads up? In that case the odds of all fifteen coins being heads up is 1/32,768. There is still only one way you can get all heads. There are 32,767 ways of getting “not all heads”. From this example we see that the odds of fall drastically as the number of joint occurrences increases.

Example #2. Four students go out of town for the college football game knowing that on Monday they have a math exam. None of them prepare for the test and do not show for the exam. On Tuesday they all come wanting to take the test saying that they went to the game, had a flat tire, and didn’t get back in time to take the test on Monday. The professor agrees to give them the test immediately and has each student sit in one of the far corners of the room. He announces that there will be only one question on the test. Each student receives a blank sheet of paper and a pencil. The professor writes the following question on the board: “Which tire?” What are the odds that, without prior planning or collusion, they will all give the same answer? There are four ways they can all agree out of 256 possible outcomes. What if the number of students had been eight going to the game in a van? In that case the odds of all eight students agreeing which tire blew out, without planning or collusion would be 4 out of 65,536 or .00006103515625.

The odds drop off very quickly when we are looking at “joint occurrences”. Joint occurrences are cases where all four students must agree, for example. These examples use very simple circumstances (heads or tails, four students and four tires on the car, etc.) The real world is much more complex. When talking of the origins of the universe or of life it is universally acknowledged that many highly unlikely circumstances would have had to have occurred jointly for the universe and life to have come into being by chance. This joint occurrence makes the odds astronomical against such a thing happening. The probability of life and the universe coming into existence by chance is not easy to calculate but it is generally agreed that the odds are extremely small.* If it was not by chance then it must have been designed or arranged.

Observation: Some believe that even highly unlikely events will eventually take place given enough time. Is this true? For more on this see the study entitled “Chance and Intelligent Design Part 4 dealing with the difference between independent and dependent events and probability.

* Richard Dawkins, staunch evolutionist and popular writer calculates that the odds of the DNA code developing twice by chance is one in a million, million, million, million, million. A River Out of Eden: A Darwinian View of Life by Richard Dawkins, p. 12.

Exercises:

Explain why the probability of joint occurrences drops off as the number of possible outcomes increases.

Come up with an example of your own showing the unlikelihood of joint occurrences.

If the probability of the DNA code developing independently twice is one in 1030, what would be the odds for it developing just once? Would you consider this a good probability?