I want to know, but I lack the resources for figuring it out. Here’s the data: roughly 90 billion people who have been born on earth have died. Roughly 7 billion people (all those who are alive today) have not. That’s over 7 percent of people who have ever been born who have not died. So, pretty good odds I’ll die someday (though of course I most resemble those who have not ever died), but not astronomically high. Except that all those alive today are in stages of life that at least some of the 90 billion dead were in before they died. So, how do I calculate this?
Here’s a relevant analogy (after the fold):
Suppose you and your friend are drawing balls from a tub and you notice that all of the ones you’ve drawn have the following pair of features: they start out red and then, at some point between 10 and 20 minutes after being withdrawn from the tub, turn green. Suppose you draw roughly 90 such balls from the tub and all of them share these two features. Now you draw 7 more balls from the tub. Your friend doesn’t look at the balls. You do. You see that they are red (as were the previous 90 balls). How certain should you be that the balls will end up green? Both you and your friend should be fairly certain; you should assign the proposition that the 7 new balls will end up green a very high probability. But your friend’s probability should be higher than yours. After all, as far as your friend knows, the balls are already green; they might just be normal green balls that end up green. But you know that, if the balls are normal balls, then they are normal red balls that end up red. So, the probability for you that the balls will end up green is lower than it is for your friend. After 20 minutes, if your friend looks and sees that the balls are now green, your friend should assign an even higher probability to the proposition that the 7 new balls will end up green. So, in turns of relative probability assignments, the proposition that the balls will end up green is the highest for your friend after your friend looks at them after 20 minutes. It is the second highest for your friend before your friend looks. And it is the third highest for you while you’re looking at them before 10 minutes is up and you see that they are red.
Suppose that the number of balls initially picked is not 90, but is 90 billion. And suppose that the number of new balls picked is not 10, but 7 billion. Here, the probability for each of you that the 7 billion new balls will all turn green is much higher. But the relative probability assignments remain the same: it is highest for your friend after looking after 20 minutes, second highest for your friend before looking, and third highest for you, when you look before 10 minutes is up and see that they’re all red
What are the relevant probabilities for you, and for your friend both before and after looking? Is this something that can be calculated without additional information?