h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I'm unsure of the origin's of this paradox, but I found it whilst leafing through a philosphy textbook:
In a hypothetical lottery, 1000 tickets are sold and distributed. The probability of ticket number 1 winning is 1/1000, ticket number 2's probability is 1/1000 and so on...
However, one ticket will win the lottery, that is a certainty i.e. there is a probability of 1.
Therefore, one ticket has a probability of 1/1000 and 1, whilst all of the other 999 tickets have prbabilities of 1/1000 and 0.

Rgds,
Kenrick

This seeming paradox is based on a complete mis-identification of what probability was, and is.

Probability was inverted so that the mathematicians involved could cheat at cards (now everyoneuses it for that, so it isn't regarded as cheating).

It deals with just one type of uncertainty, the uncertainty of inference, where you know that one of the set of possibilities is true, and only one is true, but you don't have the information to resolve which is which.

The seeming paradox arises due to the bundling together of unrelated aspects of the problem.

1, out of the set of tickets, one of them has to win. (assuming that all permutations go into the hat)

2, Given that one has to win, which one will it be.

3, in some cases, which permutation gives me the best chance of winning, or the chance of winning the most.

The conditions you have set up say that all permutations (in the general case) are in the hat. they also say that one of the tickets will definately win, but they say nothing to help reduce the uncertainty about which ticket is likely to be the winning ticket, and thus probability is not really relevant.

Note: this entire paradox only seems to make sense at all if you believe that everything is either true or false, and thus use the traditional boolian logic typical of aristotle.

If you use the multivalued logics of fuzzy logic, it obviously does not make sense, and thus doesn't appear to be a paradox.