Question 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?

Accepted:
October 10, 2013

Comments

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 their inevitable death: they prepare a will and maybe purchase life insurance for the benefit of their survivors.