Hi,
I'm sorry for not using the correct terms, but I have a problem that involves multiple layers of probability that I could solve by myself eventually, but it would take days of manual labour to systematically work through, so there must be a faster way. I would very much appreciate any advice on how to create an equation to address this puzzle.
Imagine a game where a letter is posted to a random address. The recipient of that letter will then forward it to a new address, and so on and so. The letter begins its journey by being sent to an address in London.
The probability that a letter received in London will be sent to a new address in London is 50%, that it will be forwarded to an address elsewhere in the UK is 30%, sent to an address abroad is 16% and lost for good in the postal system 4%.
The probability that a letter received elsewhere in the UK will be sent to an address in London is 10%, sent to an address elsewhere in the UK is 80%, sent abroad 7% and lost for good 3%.
The probability that a letter received abroad will be sent to an address in London is 2%, elsewhere in the UK 1%, to an address abroad 92% and lost for good 5%.
I would need to calculate the probabilities that, after 26 trips, the letter:
1. Will have disappeared
2. Will have disappeared specifically from an address in London
3. Will have disappeared specifically from an address abroad
I could easily calculate specific probabilities, i.e. the probability that it would move to London to abroad, then elsewhere in the UK, then back to London, then abroad, etc; but the complexities of this puzzle escape me. Likewise, I could manually figure this out if there were only three or four trips involved, but 26 is too many. If someone could please provide a hint on how to get moving with this then I would be extremely grateful.
Thank you in advance
I'm sorry for not using the correct terms, but I have a problem that involves multiple layers of probability that I could solve by myself eventually, but it would take days of manual labour to systematically work through, so there must be a faster way. I would very much appreciate any advice on how to create an equation to address this puzzle.
Imagine a game where a letter is posted to a random address. The recipient of that letter will then forward it to a new address, and so on and so. The letter begins its journey by being sent to an address in London.
The probability that a letter received in London will be sent to a new address in London is 50%, that it will be forwarded to an address elsewhere in the UK is 30%, sent to an address abroad is 16% and lost for good in the postal system 4%.
The probability that a letter received elsewhere in the UK will be sent to an address in London is 10%, sent to an address elsewhere in the UK is 80%, sent abroad 7% and lost for good 3%.
The probability that a letter received abroad will be sent to an address in London is 2%, elsewhere in the UK 1%, to an address abroad 92% and lost for good 5%.
I would need to calculate the probabilities that, after 26 trips, the letter:
1. Will have disappeared
2. Will have disappeared specifically from an address in London
3. Will have disappeared specifically from an address abroad
I could easily calculate specific probabilities, i.e. the probability that it would move to London to abroad, then elsewhere in the UK, then back to London, then abroad, etc; but the complexities of this puzzle escape me. Likewise, I could manually figure this out if there were only three or four trips involved, but 26 is too many. If someone could please provide a hint on how to get moving with this then I would be extremely grateful.
Thank you in advance