# Math buffs: A probability question for you.
**URL:** https://boards.straightdope.com/t/math-buffs-a-probability-question-for-you/651487
**Category:** Factual Questions
**Created:** [February 27, 2013, 3:18am UTC](https://boards.straightdope.com/t/math-buffs-a-probability-question-for-you/651487 "2013-02-27T03:18:35Z")
**Posts on this page:** 6
**Page:** 2
### Author:  [@Grrr](https://boards.straightdope.com/u/Grrr)
#### Post date: [February 27, 2013, 3:07pm UTC](https://boards.straightdope.com/t/math-buffs-a-probability-question-for-you/651487/21 "2013-02-27T15:07:10Z")
> [@deltasigma](#):
>
> Shakes: sorry about before. rough night. I should probably quit while I’m behind but that would be too easy.
>
> My first response would really be to fuck the machines. Put all of the widgets in one cabinet and overide the lock. IOW, jumper it so that even when the door is open, it thinks that it’s closed. Then, when it tells you to go to another cabinet, you dutifuly go there and open the door like a good human, reach in, grab the imaginary widget close the door then get the actual widget from the other cabinet and go about your business.
>
> When it tells you to go to the live cabinet, unjumper the lock so it thinks the door has been opened, grab the widget, re-jumper the lock, rinse, repeat as necessary. When the live cabinet happens to lock up, no big. The door is open anyway, just remember to go back at some point and pretend to “open” the door.
>
> I’m sure you’ve thought of this already and things like rules and supervisors and what not have perhaps frowned on the idea.
>
> I was wondering if the order of the widget requests are random. The locking of the cabinets may be random in terms of order, but duration and frequency has some loose parameters it seems.
>
> If not, and each cabinet is equally likely to lock first each day, then doing a 1/3 split gives you 1/6th chance of being screwed first thing in the morning or 5/6ths of -(screwed). After that it will depend on the weightings I suppose.
>
> If the same cabinet only relocks 1 time in 4, then I think you have to use [Bayes theorem](http://en.wikipedia.org/wiki/Bayes%27_theorem) - which is actually pretty simple, but I’m much to fried to attempt that right now. If I’m on the right track though, someone should be along who can walk you through it in plain English with some very basic algebra.
Whew, OK now you’re making sense. 🙂
The fault is partly mine.
The OP is a real life situation. To make my work situation understandable to the lay person, I analogized it as I did in my OP.
The “Cabinets” are actually machines. Machines designed to hold these “Widgets”. These widgets are sensitive material. They can not simply be stored outside the machine. Nor can these expensive machines be jerry rigged to keep the doors open.
And truth be told, they don’t actually randomly “lock” their doors. What they do, is break down a lot. When they do break down, it usually takes a tech an hour to get it back up and running again. During that hour we are unable to retrieve the widgets.
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### Author:  [@deltasigma](https://boards.straightdope.com/u/deltasigma)
#### Post date: [February 27, 2013, 3:37pm UTC](https://boards.straightdope.com/t/math-buffs-a-probability-question-for-you/651487/22 "2013-02-27T15:37:26Z")
So basically you were dumbing it down for me. Uh huh. I see. Well, don’t do me any fuckin’ favors, m’kay bud? (kidding 🙂 🙂 )
But it’s good for me to be reminded of my social ineptness with some regularity. Here for example, I should have tried to look a little past the exact literal facts and tried to think a little about what might have been behind them being aware (in theory at least) of the limitations of this medium.
And no I’m not just putting myself down for sport, I need to do this from time to time so it sinks in. Some people need to practice juggling more than one ball at a time. And I’m going to get right on that, probably tomorrow. :smack:
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### Author:  [@Rand\_Rover](https://boards.straightdope.com/u/Rand_Rover)
#### Post date: [February 27, 2013, 11:47pm UTC](https://boards.straightdope.com/t/math-buffs-a-probability-question-for-you/651487/23 "2013-02-27T23:47:04Z")
> [@ZenBeam](#):
>
> It sounds like you’re looking for the probability of getting through a day without “getting screwed” even once. If the computer will ask at least every hour, and\*\* if each cabinet will be locked at least once per day for an hour\*\*, then you are guaranteed to be screwed at least once per day if you put all the widgets in a single cabinet.
>
> If you spread them out, you’ll have some chance of getting through a day without getting screwed. The expected number of screws per day won’t change, though.
The bolded part above is what makes your problem different than the OP’s problem (and therefore your solution different than the OP’s solution).
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### Author:  [@The\_Controvert](https://boards.straightdope.com/u/The_Controvert)
#### Post date: [February 28, 2013, 1:08am UTC](https://boards.straightdope.com/t/math-buffs-a-probability-question-for-you/651487/24 "2013-02-28T01:08:31Z")
> [@Shakes](#):
>
> Whew, OK now you’re making sense. 🙂
>
> The fault is partly mine.
>
> The OP is a real life situation. To make my work situation understandable to the lay person, I analogized it as I did in my OP.
>
> The “Cabinets” are actually machines. Machines designed to hold these “Widgets”. These widgets are sensitive material. They can not simply be stored outside the machine. Nor can these expensive machines be jerry rigged to keep the doors open.
>
> And truth be told, they don’t actually randomly “lock” their doors. What they do, is break down a lot. When they do break down, it usually takes a tech an hour to get it back up and running again. During that hour we are unable to retrieve the widgets.
Sounds like you need more redundancy. But since you’re probably not allowed to put your material on multiple machines and I’m guessing you can’t implement things like RAIDs to improve server reliability, then it doesn’t matter where the widgets are distributed.
However, in real life there are other factors to consider. If a particular widget is unavailable, can a user request another widget to work on while waiting? If so, then you don’t want to put them all in the same cabinet.
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### Author:  [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)
#### Post date: [February 28, 2013, 1:55am UTC](https://boards.straightdope.com/t/math-buffs-a-probability-question-for-you/651487/25 "2013-02-28T01:55:56Z")
> [@Rand\_Rover](#):
>
> The bolded part above is what makes your problem different than the OP’s problem (and therefore your solution different than the OP’s solution).
I thought he had said they locked at least once a day, but the closest he came was saying
> [@Shakes](#):
>
> However, a cabinet is less likely to lock itself more than two or three times a day.
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### Author:  [@brickbacon](https://boards.straightdope.com/u/brickbacon)
#### Post date: [February 28, 2013, 5:09am UTC](https://boards.straightdope.com/t/math-buffs-a-probability-question-for-you/651487/26 "2013-02-28T05:09:53Z")
Wouldn’t it always be a matter of choosing between variance and stability? As a thought experiment, let’s compare a situation where all 1000 widgets are in one machine vs. a hypothetical where they are in 1000 different machines (one widget per machine). If we accept that each will lock 1 hour per day, the first scenario ensures one break down per day, but only one per day. The latter, on a good day, will likely not breakdown, but on a bad day, you could be down essentially all day.
The only wrinkle is that multiple machines can be locked at once. Seeing that that can happen I would lean slightly towards putting them all in one because you get less upside from spreading them out if all the machines could theoretically be locked simultaneously.
I think it would come down to a few outside factors like:
1. Do the machines “lock” as a result of use/overuse
2. Can multiple machines be fixed at once?
3. Are the machines serviced or replaced at a regular interval w/o regard to use.
4. Are the repair people on call or on site?
5. Can you mitigate the lost labor costs during downtime if you knew roughly when it would occur?
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