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Okay, here's a simplified probability tree. Scenario 1: Doom soon 10 people have a room number less than or equal to 10. Scenario 2: Doom late 10 people hav

Okay, here's a simplified probability tree. Scenario 1: Doom soon 10 people have a room number less than or equal to 10. Scenario 2: Doom late 10 people have a room number less than or equal to 10. --- Given that each scenario has an equal probability in isolation, there are 20 possible positions for the the <=10 individual to find themselves in (10 in doom soon, 10 in doom late). Of those 20 possibilities, 10 of those are in the doom soon scenario. The remaining 10 are in the doom late scenario. 10 doom soon to 10 doom late is a 50/50 probability. Edit: writing up a script as well, right now. Will add to link to it in my original comment when complete.

rm445 12y ago
You're wrong. Not being mean, you've just arrived at the wrong numerical answer to the maths question. (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.
- livingparadox 12y ago
  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.

rm445 12y ago

You're wrong. Not being mean, you've just arrived at the wrong numerical answer to the maths question. (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.

livingparadox 12y ago
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.