# Is there any way to define coincidences so as to make their existence possible in a deterministic world?

### I think so. Suppose you

I think so. Suppose you encounter an old acquaintance, whom you haven't thought about in years, on a street corner in a foreign city. That unexpected encounter sounds to me like a paradigm case of a coincidence, precisely because it was (as we say) "the last thing you were expecting." Nevertheless, the encounter might well have been guaranteed to occur by prior conditions, as determinism says all events are. Our very limited knowledge of the prior conditions -- indeed, our total lack of interest in their precise details -- makes such an encounter surprising, i.e., not at all predictable by us given how little we knew about the prior conditions. Even so, those prior conditions could have determined that the encounter would occur exactly when, where, and how it did.

# If the probability of death is 100%, and the probability of being alive tomorrow is uncertain, does that mean the probability of dying tomorrow is greater than the probability of being alive? If so, why am I so convinced that planning for the future is a good thing? People seem to spend large amounts of time planning for their future lives, but shouldn't they be planning for their unquestionable death?

If the probability of death is 100%, and the probability of being alive tomorrow is uncertain, does that mean the probability of dying tomorrow is greater than the probability of being alive? No. Let death be represented by a fair coin's landing heads-up. The probability that the coin will land heads-up at least once in the next thousand tosses is essentially 1 out of 1 (it differs from 1 only beyond the 300th decimal place). It's also uncertain that the next toss will land tails-up. Yet those facts don't imply that the probability of heads on the next toss is greater than the probability of tails: it's a fair coin, we're assuming. Or imagine a lottery with one thousand tickets, exactly one of which is the winning ticket. You have all the tickets gathered in front of you but don't know the winning ticket. There's a 100% chance that the winning ticket is gathered in front of you but only a 0.1% chance that the next ticket you touch is the winner. Nevertheless, responsible people do plan for...

# Suppose that you had two bags each with an infinite number of blue marbles. Suppose you also had another bag of infinity red marbles. If you mixed those three bags what are your odds of getting a red marble? Obviously this isn't a realistic experiment but is it 1 in 3 or 50%?

The intuitive answer seems to be "1 in 3," and I think that's the right answer if each infinite set of marbles has the same size (or "cardinality"). I take it you're wondering if the infinite size of the sets invalidates the intuitive answer. I don't think it does. Maybe this analogy will help. There are infinitely many even whole numbers and infinitely many even plus odd whole numbers, but there aren't twice as many of the latter as there are of the former: the cardinality of the two sets is the same. Yet the odds that a randomly chosen whole number is even are surely only 1 in 2 (rather than 1 in 1). If that reasoning is sound, then the fact that the various sets are infinite doesn't affect the probability.