Nick Bostrom

So suppose

So suppose

I have two urns, and I fill one urn, or I put 10 balls in one of the urns, and the balls are numbered from 1 to 10.

I have two urns, and I fill one urn, or I put 10 balls in one of the urns, and the balls are numbered from 1 to 10.

And then in the other urn, I put a million balls numbered from 1 to 1 million.

And then in the other urn, I put a million balls numbered from 1 to 1 million.

Then let's say I flip a coin and select one of these urns and put it in front of you.

Then let's say I flip a coin and select one of these urns and put it in front of you.

And now your task is to guess how many balls are there in this urn.

And now your task is to guess how many balls are there in this urn.

So at this point you say 50-50 that there is a million balls, right?

So at this point you say 50-50 that there is a million balls, right?

Because one of each urn and selected one randomly.

Because one of each urn and selected one randomly.

Okay.

Okay.

Now let's suppose you reach in and select one random ball from this urn and it's number eight, let's say.

Now let's suppose you reach in and select one random ball from this urn and it's number eight, let's say.

So, using Bayes' theorem, that allows you to infer that it's now much more likely that the urn has only 10 balls than a million.

So, using Bayes' theorem, that allows you to infer that it's now much more likely that the urn has only 10 balls than a million.