5 ms·

It's probably not worth worrying about the fate of humanity till you've figured out the rooms example. Since you're on this site I'm sure you can trivially knoc

by rm445 12y ago

It's probably not worth worrying about the fate of humanity till you've figured out the rooms example. Since you're on this site I'm sure you can trivially knock up a script to simulate what happens. Or just draw the probability tree. In any case the relevant question is,, 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. The answer is 90.9% - we could go round in circles trying to choose words that everyone understands, but the numbers speak for themselves.

livingparadox 12y ago
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.
livingparadox 12y ago
Here's a simulation to test this argument. http://jsfiddle.net/3f49ry5u/ http://jsfiddle.net/3f49ry5u/ So... unless I did the simulation wrong, it supports my conclusion. If I did do it wrong, please show me a corrected simulation which supports your position.
- rm445 12y ago
  Sorry amigo, I gotta get to work. Here's my code I wrote last night, hope it makes sense: http://pastebin.com/79rmjmKr http://pastebin.com/79rmjmKr Typical result: 494644 results in rooms less than 10: 449838 had 10 rooms (90.9%), 44806 had 100 rooms 9.1% Note that anyone who finds themselves in a high-numbered room can draw the obvious conclusion. The question is, what can you infer about the situation if you find yourself in a low-numbered room? To hammer the point, let say the coin toss decides between 1 room and ten million. If you find yourself in room One, do you still think the chance the coin has come up heads is 50%? If you do, don't tell me, write a letter to Monty Hall. My vague ponderings about the actual doomsday problem is that it holds up, i.e. it's a reasonable argument that it makes eventual populations of say 10^400 simulated souls using the whole universe as a computer highly unlikely. But the sheer bigness of the possible-but-unlikely population leaves plenty of room for astronomical-sized future populations and doom isn't necessarily imminent in human terms.

by rm445 12y ago

livingparadox 12y ago

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.

livingparadox 12y ago

Here's a simulation to test this argument. http://jsfiddle.net/3f49ry5u/ http://jsfiddle.net/3f49ry5u/ So... unless I did the simulation wrong, it supports my conclusion. If I did do it wrong, please show me a corrected simulation which supports your position.

rm445 12y ago
Sorry amigo, I gotta get to work. Here's my code I wrote last night, hope it makes sense: http://pastebin.com/79rmjmKr http://pastebin.com/79rmjmKr Typical result: 494644 results in rooms less than 10: 449838 had 10 rooms (90.9%), 44806 had 100 rooms 9.1% Note that anyone who finds themselves in a high-numbered room can draw the obvious conclusion. The question is, what can you infer about the situation if you find yourself in a low-numbered room? To hammer the point, let say the coin toss decides between 1 room and ten million. If you find yourself in room One, do you still think the chance the coin has come up heads is 50%? If you do, don't tell me, write a letter to Monty Hall. My vague ponderings about the actual doomsday problem is that it holds up, i.e. it's a reasonable argument that it makes eventual populations of say 10^400 simulated souls using the whole universe as a computer highly unlikely. But the sheer bigness of the possible-but-unlikely population leaves plenty of room for astronomical-sized future populations and doom isn't necessarily imminent in human terms.