## Probabaility of remaining at large...

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didds
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### Probabaility of remaining at large...

https://www.washingtonpost.com/blogs/wo ... 00b5dce556

(Im not planning a career change incidentally!)

" his chances of eventually getting caught will increase: at 0.8 probability per raid, after three raids or a year and a half his odds of remaining at large are 0.8 × 0.8 × 0.8 = 0.512; after four raids he is more likely than not to be inside. "

That is not very clear but I THINK it means the chances of NOT being caught are 0.8 ie 80%. Because iof it was 0.8 to be caught - on the logic of the above the more bank raids one does the LESS chance of being caught

However its the logic that I'm questioning..

If the probability of NOT being caught are 0.8 per raid, after three raids he is still at large. The probability of being caught has been "beaten" so to speak. So isn't the fourth bank raid just a one hit 0.8 chance of remaining not caught again? ie historical context redundant. The 0.8 chance has been true three times. That's why he can attempt a 4th.

IF of course the 0.8 does mean the chances of being caught... the same applies. He got the 0.2 chance three times. Now he is into a fresh 0.8/0.2 chance .

??

didds

nmdhqbc
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### Re: Probabaility of remaining at large...

didds wrote:I was just reading this

https://www.washingtonpost.com/blogs/wo ... 00b5dce556

(Im not planning a career change incidentally!)

" his chances of eventually getting caught will increase: at 0.8 probability per raid, after three raids or a year and a half his odds of remaining at large are 0.8 × 0.8 × 0.8 = 0.512; after four raids he is more likely than not to be inside. "

That is not very clear but I THINK it means the chances of NOT being caught are 0.8 ie 80%. Because iof it was 0.8 to be caught - on the logic of the above the more bank raids one does the LESS chance of being caught

However its the logic that I'm questioning..

If the probability of NOT being caught are 0.8 per raid, after three raids he is still at large. The probability of being caught has been "beaten" so to speak. So isn't the fourth bank raid just a one hit 0.8 chance of remaining not caught again? ie historical context redundant. The 0.8 chance has been true three times. That's why he can attempt a 4th.

IF of course the 0.8 does mean the chances of being caught... the same applies. He got the 0.2 chance three times. Now he is into a fresh 0.8/0.2 chance .

??

didds

You are correct. Once the 3 are done without failing the next probability is re-set to 80/20. "his chances of eventually getting caught will increase" - I think this quote could be interpreted in a couple of ways. They could mean increasing the number of attempt they plan to do before they start. In which case the statement is true. The probability of failing increases. If you read it as doing three then determining to do the 4th then they're wrong. It goes back to 80/20.

chas49
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### Re: Probabaility of remaining at large...

nmdhqbc wrote:You are correct. Once the 3 are done without failing the next probability is re-set to 80/20. "his chances of eventually getting caught will increase" - I think this quote could be interpreted in a couple of ways. They could mean increasing the number of attempt they plan to do before they start. In which case the statement is true. The probability of failing increases. If you read it as doing three then determining to do the 4th then they're wrong. It goes back to 80/20.

I'm not sure that this conclusion is entirely correct.

Clearly it's valid to say that (based on the stats the paper quotes) roughly 20 percent of bank raids end up with the perpetrators being caught, convicted and sentenced. That doesn't mean that 80% are successful - as there are different stats for those that got away but with no money, and those that got money, but were ultimately caught.

So we have an 80% chance (or 0.8 probability of success) for each raid. The authors simplify this a bit by proposing that the same probability applies to each subsequent attempt. I think there's probably some validity in a suggestion that a robber who has succeeded once will have slightly improved odds of success on the next attempt. I can't guess how much that might be, or how long the improvement in the chance of success would continue.

However, I can't see any reason to assert that the probability resets to 0.8 after 3 attempts. This isn't like tossing a coin where each event is entirely independent of the previous one (fair coin etc assumed). Each raid leaves some evidence and over time the robber will increase his/her chances of being caught as the evidence potentially builds up. On the other hand, s/he will be learning from each raid and becoming more proficient at it.

The probability of success might be something like .8, .75, .72, .71, .71, .71 (purely made up figures though).

I agree the authors may have over-simplified the calculation (although their main point was to demonstrate that bank robbery is not a particularly lucrative career option), but I'm not convinced it "goes back to 80/20".

nmdhqbc
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### Re: Probabaility of remaining at large...

chas49 wrote:However, I can't see any reason to assert that the probability resets to 0.8 after 3 attempts. This isn't like tossing a coin where each event is entirely independent of the previous one (fair coin etc assumed). Each raid leaves some evidence and over time the robber will increase his/her chances of being caught as the evidence potentially builds up. On the other hand, s/he will be learning from each raid and becoming more proficient at it.

Yeah, I agree with all that. I kinda just addressed the specific confusion the OP talked about rather than digging deeper into it.

didds
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### Re: Probabaility of remaining at large...

based on the simplisitic stuiff on the WP article...

it doesnt get reset after 3 attempts.

it gets reset after every attempt.

Or rather, every attempt is that same (simplistic maybe) stat. Its not a 3 strikes and you are back in the game thing.

didds

chas49
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### Re: Probabaility of remaining at large...

didds wrote:based on the simplisitic stuiff on the WP article...

it doesnt get reset after 3 attempts.

it gets reset after every attempt.

Or rather, every attempt is that same (simplistic maybe) stat. Its not a 3 strikes and you are back in the game thing.

didds

I don't agree that it ever gets reset. Based on the general stats in the paper (a little more detail that in the article), roughly 20% of bank raids end up with the perps being caught. That doesn't actually mean that an individual robber has a 20% chance of being caught each time (see my previous post) - just that overall about 20% of raids have that result.

It isn't three strikes and reset (as you correctly say), but (IMHO) neither is it "that same stat" every time.

Lootman
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### Re: Probabaility of remaining at large...

Where does the 80/20 number come from anyway? Do they count the number of robberies and the number of suspects caught? What if two men rob a bank, and one is caught and one is not? How do they even know how many robbers there were (including a getaway driver? Suppliers and co-conspirators who weren't actually at the bank? And so on).

And bank robberies are a favourable case because they presumably all get reported and counted. With many crimes there is really no way to know how often they happen. For instance how often do people double park? Fiddle their taxes? Take items from shops without paying? It can really only be guessed at.

The only people who really have an accurate idea of the success rate of a crime are the criminals themselves. Decades ago I had an upstairs neighbour who happily told me that he made a living as a burglar. It intrigued me that he was so open about it and I asked him if he ever gets caught. He replied that he'd had been caught 3 times and he had robbed hundreds of homes.

Call that a 99% success rate.

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