To understand probability, it is helpful to define a few more terms. Chance : the occurrence of events in the absence of any obvious intention or cause. Random : made, done, or happening without method or conscious decision. Probability : is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. So we see that the words "chance" or "random" can almost be used interchangeably. The Battle of Ramoth-Gilead In 1 Kings 22 we read of an interesting story that is useful for our purposes here. The prophet Micaiah had prophesied that the King of Israel, Ahab, will die in battle against Ramoth-Gilead. Ahab, trying to thwart the Word of God, decided to disguise himself in battle so the enemy cannot target him. We then read the following: But a certain man drew his bow at random and struck the king of Israel between the scale armor and the breastplate. Therefore he said to the driver of his chariot, “Turn around and carry me out of the battle, for I am wounded.” 1 Kings 22:34, ESV So, in the first place - the man drew his bow at random. We can imagine in the heat of battle someone drawing a bow and shooting an arrow in the general direction of the enemy. We also read that the arrow not only managed to hit the target, but struck in exactly the right place, where there was no armour on the king.
We would probably describe this event as random, but was it?
God showed that day that he was in charge of seemingly random events. He controlled when the man drew his bow. He controlled the direction of his aim. He controlled the moment the arrow was released. He controlled the flight of the arrow. He controlled the way Ahab’s armor was put on earlier in the day, and the position that Ahab took as the arrow came nearer. He controlled the arrow as it struck in just the right spot and went in deep enough to produce fatal damage to organs. He brought Ahab to his death . It is true that the God that acted in the time of Ahab is the same God today, and is still in control of all events we would call "random". Randomness and probability What we as Christians called "randomness", is in actuality only perceived randomness. There is nothing that happens that escapes the decree of God in creation. So, in a sense, there is no randomness. Yet, in another sense, there seems to be from our perspective . As we are finite creatures, we cannot possible know the intention of God in every circumstance or event. We are limited to His revealed will in Scriptures - and that is that He works all things for the good of those who love Him. So, what is probability? We know that God doesn't work in probabilities as His knowledge of the future, the past and present is based on His decree. The interesting thing about the world we live in (as created by God), as that it consists of both uniformity and unpredictability. It is only because these two items are held in balance that any study of probability makes sense (refer back to part 2 ).
The for example the toss of a coin. In this case we can define a probability distribution of a coin toss (a concept which we'll discuss in full when we reach part 4) as The probability distribution of the coin toss remains uniform. It is always the case (all other things constant), the the above probability distribution function will hold for any good and proper coin toss. Poythress mentions that this regularity in something as simple as a coin toss actually expresses the faithfulness of God . If the stable context that surrounds the coin changes (e.g. someone changes the coin's features mid-air, or changes the spin velocity manipulating it in each throw), the probability distribution fails. But that's not how God created the universe. Now, here is the kicker. Every probability we assign is a human approximation of God's ordained outcome of an event. Every coin flip has been determined when God decreed to create. He specified the predictability of the coin toss, as well as the unpredictability inherent in every specific coin toss. We cannot predict in advance exactly how a coin or dice will fall. We cannot predict exactly what the weather will look like tomorrow. But we can predict that a coin or dice will fall in a regular pattern. We can predict that the weather will come and go in uniform seasons. [God's] control is not an “interference” with a situation that is allegedly operating purely under its own autonomous power. We may conclude that [He] specifies both the generalities and the details, the predictabilities and the unpredictabilities. He specifies it all. And because his word has his power, his specification is effective... ... The particulars about one roll of the dice go together with the generalities about all dice rolls. Why? God specifies it all, and it all expresses his wisdom, in the particulars and in generalities. We can praise him for it all. Poythress, Chance and the Sovereignty of God, pg. 104 There is no such thing as chance. There is no such thing as randomness. From a human perspective, there is only perceived chance and randomness. Probabilities only make sense if we have a sovereign Creator-God that specifies predictability and unpredictabilities in a harmonious fashion. If there is no regularity in the midst of irregularity, statistics becomes an useless subject of study. So, in conclusion, probabilities are human approximations of God's created patterns. Recap We started off with an introductory remark on actuarial apologetics . Thereafter we discussed some entry level statistics so the reader can get a feel for the field. This is the first time we've approach the subject from a distinctly Christian view. The reason for this, is that we went beyond mere observation. We started to ask meta-level questions on probability itself. It is unfortunate that when statistics and mathematics is taught in schools or universities, it is divorced from a worldview that provides a context for the study of mathematics and statistics to be meaningful. Most people assume these things make sense on a surface level without digging deeper to the meta-level. I hope to change this - at least for myself as I think through these posts. References  S., V., 2014. Chance and the Sovereignty of God . Crossway. pg. 34. [https://frame-poythress.org/wp-content/uploads/2014/07/ChancePoythress.pdf]  S., V., 2014. Chance and the Sovereignty of God . Crossway. pg. 147. [https://frame-poythress.org/wp-content/uploads/2014/07/ChancePoythress.pdf]