How Much Chance in “Chance”?
A REAR door of the huge airliner mysteriously rips open in midair, depressurizing the cabin and killing 300 people when it drops to the earth, a flaming wreck. What are the chances—the odds —that you could have been on that plane?
Or suppose that you have been playing bridge all evening without once being dealt the ace of spades. What are the chances that you will get this card on the next deal?
Then there is the student who sits in a university classroom and hears a professor say: “According to the law of averages, evolution had to take place . . .” But, the pupil wonders, “Did it?”
“Chance”—often we use that word to mean no more than an accidental happening, and it is indeed correctly employed in this manner. But as these examples show, it has another meaning. It brings to mind the subject of probability. This subject is not just something for mathematics experts, though they particularly relish the intricacies more than others.
Learning Probability from a Coin
To appreciate the applications of probability, let us consider it at its fundamental level.
Flip a coin into the air. Will it land heads or tails? No human can unerringly predict. Flip the coin ten times. How often will it come up heads? Again, no human can foresee.
But just suppose that you took time to flip the coin two million times. Then how often will it land heads? About one million. Yes, for reasons that cannot be fully explained by men, the coin, over the long haul, will land half the time heads up.
True, in any short test, you do not know for a certainty whether heads or tails will turn up. It may be flipped, seven times out of ten, heads. But next it may turn out to be seven times tails. The more times the coin is flipped, the closer it will approach its natural average of 50 percent heads and 50 percent tails. This is called “the law of large numbers.”
But the odds for any single toss are still one in two that it will come up heads. On the second toss the odds are precisely the same for that single toss, one in two. Any time that you toss it, the odds for that one toss remain precisely the same. You see, the coin has no memory. But, suppose that someone wants three heads in a row to come up and no tails? What are the odds?
Just multiply together the chances of getting heads on each toss. For one toss the likelihood of tossing heads is one in two or 1/2. For two tosses, thus, it is 1/2 times 1/2, or odds of one in four. Three tosses is 1/2 times 1/2 times 1/2, or odds of one in eight, and so on. There are other ways that the same basic mathematical laws rub off on your life.
Chance in Gambling, Insurance and Flying
For one thing, a basic knowledge of the law of large numbers can keep you from naïvely thinking that you can really win at gambling. In the long run you cannot.
In a casino, there may be a roulette wheel with a series of alternating red and black numerals, 1 through 36; there is also one white zero (0) and a double zero (00). The idea is to bet on one number and, if you win, the casino will give you thirty-five times as much as your bet. But probability reveals that this is a poor risk.
To prove this, imagine yourself placing a one-dollar bet on each of the 38 numerals. Only one of them can win, and so for your $38 investment you get back $35, plus your original dollar placed on the winning number. The difference, two dollars, which amounts to over 5 percent, is in the casino’s favor. That is why it can stay in business, pay its employees and afford fancy decor. True, a customer may hit on a winning streak and win several thousand dollars in one evening. He might do it again for two, three or four evenings. But the casino knows that in the long run it must win. The laws of probability surpass a full 5 percent in its favor. No, in the long run you cannot really win.
The law of large numbers also helps insurance companies to set their rates. A customer regularly pays a relatively low sum to a company and it, in turn, pays the customer a certain amount at the time of an emergency. The insurance companies know from experience that they will not have to pay off all clients. How can they be so sure?
Life insurance companies, as an example, study the mortality rates of thousands of persons and determine what percentage of persons in each age group die annually. Knowledge of this percentage is the basis for determining the rates that each group pays for its insurance; only a certain percentage, the rates indicate, will have to be paid off in varying amounts through the years.
However, when someone wants a special insurance, as when a dancer wants her legs insured, the rates are much higher. Why? Because there are just a few of such cases; the law of large numbers is restricted. The risk is greater to the insurance company. Again, it is like flipping a coin. When the insurance company will be, so to speak, flipping the coin thousands of times, the odds are in its favor. But when there is only one flip, the risk is much greater. So the insurance rates are much higher.
Do not conclude that holding insurance and gambling are the same; rather, the same laws affect both subjects. In gambling you might win whether you need the money or not. But with insurance you “win” only to cover a loss on your part.
Really, “chance” for the average gambler usually means nothing more than blind “luck.” He may know nothing about any law of large numbers, but he earnestly hopes that somehow the right combination happens to appear while he is gambling.
An accurate knowledge of the laws of chance may also relieve your mind before you board an airplane. In 1973 there were over four and one half million commercial airline flights by U.S.-owned airplanes. And there were three crashes with fatalities. That means that there was one crash for every one and one half million flights. Every time someone got into an airliner the odds were precisely the same: one in 1,500,000 that it would crash with deaths.
By careful math, a person may reason that the first of three crashes would occur near the end of one and one half million successful flights or, in other words, after about four months. So he might avoid that flight. But, in reality, all three of the 1973 fatal flights took place within a nine-day period in July.
Now, just assume that the same basic percentage of fatal flights continues to hold true. No one can say when they will occur. Will twelve planes fall in one day, followed by a four-year period with no crashes? Who can say?
Therefore, you can confidently board an airliner with the assurance that no fatalistic “law of averages” is out to get you.
Does Chance Favor Evolution?
Understanding the elementary concepts about probability that we have discussed helps us to appreciate the fallacy of believing that chance favors life starting by accident and then evolving into the diverse forms now covering the earth.
It might be asked, however: If all the chemical “ingredients” needed to form life by accident were mixed in enough different ways over a long period of time, would life not eventually occur? Well, to begin with, someone or something must do the mixing. But, for the sake of discussion, let us purposely overlook that necessary requirement and consider: In one cell there are thousands of tiny molecular and chemical actions going on. And, in a human there are trillions of cells, some of them performing extremely specialized functions. The chance that these processes started and evolved by a mindless mixing is fantastically remote.
Let us illustrate what we mean, using a deck of cards.
Suppose you are playing bridge. What are the chances of having all 13 spades in a 52-card deck dealt to you? The odds that on the first card drawn you will get a spade are, obviously, 13/52. Of the 51 cards left, 12 are spades, and so the odds become 12/51. And so on, 11/50, 10/49, right on down to 1/40 for the final card. Multiply all of these fractions together and you will find that the chance of being dealt all 13 spades is one in over 635,000,000,000.
And, remember, we are dealing with a mere 52-card deck.
Further, we are not asking the deck of cards to give us the spades in their correct numerical order. That requirement would compound the probability manyfold. Yes, the odds then become 1/52 to start with and not 13/52. If the right card is dealt the first time, the odds then become, not 12/51 but 1/51; then 1/50 (not 11/50), and so forth. The total probability of drawing all of the spades in order would be the result of multiplying all of these figures together: 1/52 x 1/51 x 1/50 x 1/49 x 1/48 x 1/47 x 1/46 x 1/45 x 1/44 x 1/43 x 1/42 x 1/41 x 1/40. What kind of odds does that give?
One in about 4,000,000,000,000,000,000,000.
That is for just thirteen “ingredients” lined up in the right order. Do not forget that each ingredient already exists, according to this argument, and, somehow, in just the right amount. In other words, we are saying the deck of cards exists before we start.
Another thing: two sexes would be required for advanced life to continue. So the same process must happen, not just once, but twice. What are the chances that you can draw thirteen spades in proper numerical order out of the deck of cards two times in a row? To find out, it would be necessary not just to add the above figure twice, but to square it, that is, multiply it by itself. That would be one in 16 followed by over forty zeros.
There are, of course, many, many more operations involved with a pair of living humans than the mere shuffling of thirteen ingredients. But does not this vividly illustrate how remote the chances are for life starting by accident and then following an evolutionary trail?
Actually, the chances are so dim that even avowed evolutionists acknowledge it is all but impossible to believe. Says Julian Huxley: “A little calculation demonstrates how incredibly improbable the results of natural selection can be when enough time is available.” He asks, What are the odds that a horse could be produced by chance alone? In his answer Huxley refers to “the fantastic odds against getting a number of favorable mutations in one strain through pure chance alone,” and then he adds: “A thousand to the millionth power [1,0001,000,000], when written out, becomes the figure 1 with three million noughts after it; and that would take three large volumes of about five hundred pages each, just to print! Actually this is a meaninglessly large figure, but it shows what a degree of improbability natural selection has to surmount . . . One with three million noughts after it is the measure of the unlikeliness of a horse—the odds against it happening at all. No one would bet on anything so improbable happening.”
Nevertheless, Huxley turns around and incredulously says: “Yet is has happened.” How consistent does that seem to you? If anyone wishes to believe odds of that nature, that is his foolish decision. But he cannot honestly say that the burden of evidence—the odds—rests with his case.
Or Does “Chance” Point to a Designer?
On the other hand, have you not always known life to come from other life? Surely. Your own experience, then, tells you that “chance” favors life as having been started by a living Creator. In this observation you are backed up by the whole concept of probability. Why do we say this?
Because probability indicates design. The laws of probability, which we have only partially examined, are the basis of virtually all scientific thought. Men thoroughly trust these inanimate laws. So constant are they that scientists say that we can put “faith” in them. Now, are we to believe that such laws exist purely by accident? Or, do not laws have lawmakers? Certainly the weight of data, the odds, point to a Designer behind mathematical laws. Further, if these laws and others of material creation are so constant, unchanging, then the Creator must be the same.
There is genuine pleasure in coming to understand the precision workings of laws like those of probability. But the truly discerning person wants more than that satisfaction. He wants to come to know the One who made such laws. Such an experience can be infinitely more pleasurable.
[Picture on page 23]
The figure showing the odds that evolution could produce a horse would fill three large books. Would you place faith in such odds?