The fact is that probability only has meaning with respect to ignorance of a particular set of circumstances. The random letter calculator (why did anyone think that was worth setting up?) can be predicted to have a 100% chance of generating a 50 letter sequence. It can also be predicted to have a 0% chance of generating a 50-letter word, because none exist in English.
Presumably the number of three-letter English words can be extracted from a dictionary, and that number compared with the total number of possible three-letter sequences to give probabilities that any partiicular number of English words will occur in a single run. We could also predict the likelihood any particular word.
We then discover that âeggâ has appeared on the test run. Since there is no ignorance about its appearance, its probability is, trivially, 1. But that does not tell us how often it will turn up.
But we could still, using our previous figures, estimate the probability of its happening again under the same circumstances - producing a very low figure - and since the circumstances are the same, we can use the same figure to deduce how likely it was to have appeared the first time, before the event.
That, of course, presupposes ignorance of the actual causes at work (for chance is not a cause, but only a measure of ignorance about cause), meaning that we have assumed each letter appears equally frequently. But if we werenât ignorant in that way, there would be no point in a probability calculation anyway. We could instead simply examine whether the causes available would ever produce âeggâ, and when, and the probability would be either 1, or 0.
For example, if God or a biased algorithm intends âeggâ to appear on this run, the advance probability will be, to him,1. But to us it, ignorant of that fact, it will be whatever figure we calculated.