Re:A Primer on the Doomsday Argument
by livingparadox on Monday August 18, 2014 @05:39PM
(#8194865)
Just to confirm my understanding...
The situation you gave me was "out of those who find their room number is less than ten, what is the probability that the coin toss meant only ten rooms are occupied".
In my example, I composed my tree of solely those who with a room number less than or equal to 10, since in your question, we're only concerned about those who are in rooms 1-10.
In your example, it seems you've included those who are in rooms 11-100... If we are only concerned with rooms 1-10, what relevance does the probability of 11-100 play in this role?
More specifically, your seems to be what the odds are of /being in/ room 1-10, rather than the odds of each scenario occurring, assuming you are in room 10.
(Let's leave aside mentions of doom and stick to the rooms: according to the article no-one has quite nailed down yet whether there are subtleties about unbounded future populations). Rather than try to draw a tree I'll write it out flat:
10 rooms (0.5) & you're in 1-10 (1.0): Probability 0.5
10 rooms (0.5) & you're in 11-100 (0.0): Probability 0.0
100 rooms (0.5) & you're in 1-10 (0.1): Probability 0.05
100 rooms (0.5) & you're in 11-100 (0.9): Probability 0.45
Work out any relative probabilities using the right-hand column. For instance, when you're in room 1-10, the chances of the coin having been heads is 0.5/0.55. Even if this bugs you, this approach of using the tree will let you get the right answers to tricky teasers about medical tests with false positives and false negatives.