At some point in my high school education, the school chaplain came to talk about Biblical prophecy. There was no particular occasion that I could identify - he just popped into one of my classes (maths, if I recall correctly). He didn't go into depth about the prophecies themselves, but lauched into a crackpot probability analysis of their fulfillment. Through some arithmetic acrobatics he came up with a probability of 1 in about 10120 that these prophecies could have been fulfilled by accident (give or take a few orders of magnitude; I can't remember exactly).
There was some analogy that involved counting grains of sand. I pointed out at the time that 10120 was considerably greater than the total number of atoms in the observable universe - about 1080 - which doubtless made him feel even more warm and fuzzy. I was not taken with the logic of his argument, however. Had I known more about these prophecies I may have mentioned the fatal flaw in all this.
Even if you accept the mathematics, which in itself is being exceptionally generous, there's still the little matter of deciding whether the Bible is actually true. We do know - as I understand it - that the prophecies were made before the accounts of their fulfillment were written, so the prophecies were not reverse engineered. Nevertheless, the dazzling probabilities are a little premature. All we have is second-hand information, translated and rephrased over the course of centuries by people who hardly present themselves as disinterested parties.
No independent authority has found any evidence for the fulfillment of the prophecies, and why should we expect them to? If anyone else had written a book containing both a set of prophecies and accounts of their fulfillment, nobody but the most unhinged would even think about lending it any credence. Carl Sagan's elegant quote applies: extraordinary claims require extraordinary evidence. We have no evidence at all, let alone anything we might term extraordinary.
I feel that I'm still relatively ignorant of what the Bible has to say about prophecies, but by the preceeding reasoning I shouldn't need to understand every detail of the Bible in order to dismiss the book as a whole.