# What is the probability of being drunk at work and also being tested? Let's find out! Correctly

Analytical skills are in big demand so it is really important not to make the basic, common, mistakes that show you up as a newbie. For example, probability calculations are often performed on binary outcomes such as "What is the probability that a given policy holder will claim?" The result is binary because they will either …

#### Course I'm drunk at work....

..how the hell else do I suffer this existence.

#### Re: Course I'm drunk at work....

I don't advise it. Even the wankers on the site wouldn't drink that, that's worse than meths.

Nonsense. This is a far superior drink to meths. The wankers don't drink it because they can't afford it.

#### Re: Course I'm drunk at work....

You joke, but when you daily have to deal with a so called "manager" who can't get through the day without an extended liquid lunch, it soon becomes tiresome!

#### Re: Course I'm drunk at work....

My first manager (and also the HR and catering managers) spent every lunchtime in the bar (3-4 pints daily), and had a bottle of whiskey in his desk. I don't think he ever drove home sober after work...

Define "drunk" :)

Back in the early 90's a company I worked for had a policy. The actual wording was "you must not attend work drunk to the extent of being incapable". Left quite a lot of scope for a pint or three at lunchtime (and to be fair there was no risk of working with alcohol in the system other than not getting the work done).

#### Another thing you forgot

If you test every day, employees will probably modify their behaviour so they don't get caught, or find another job.

#### Re: Another thing you forgot

Indeed. Assuming testing first thing in the morning (before you drive your train/bus/lorry into people), you will merely ensure not being too tipsy for these activities at that time.

Which leads to inevitable lunchtime drinks, and afternoon drinks, and then getting home and not drinking, because you've got to get your liver to process six pints in the next twelve hours.

This is actually a far better way to do drinking than the British 'neck a load in the evening until 1am' methodology, that guarantees a nasty hangover the next day.

the more frequently you test, the higher the chance of catching the miscreant pissing off all your staff.

Fixed it for you.

#### Am I missing something?

So taking the bag of marbles example, if I'm being tested once a week then for the first test there are 248 green marbles and 12 red marbles, (total 260), but on the 2nd test there will be 5 days (assumign 5 working day week) less surely - not 1x less? (and dont get me started on how we work out how many green/how many red we need to take out)

#### Re: Am I missing something?

"but on the 2nd test there will be 5 days (assumign 5 working day week) less surely - not 1x less? (and dont get me started on how we work out how many green/how many red we need to take out)"

I think I convinced myself that summing over all possibilities for removing n balls at random for varying n gives you the same answer as if you just remove a single green ball. I didn't prove it, but that's because I couldn't be bothered.

#### Re: Am I missing something? (I am most definately not a mathmatician)

I'm surprised it took till page 3 for me to find someone else saying this, specifically, how do you know (apart from on day 1) how many red balls are in there?

Every day, someone takes out 1 ball, but you don't know what colour it is. so there is a possibility that after say, 15 days, all 12 red have been taken out, but because they were removed on non test days, you have no idea. As the tester, every day (whether you are testing or not) there are between 0-12 red balls in the bag.

As others have said, there is a chance that people are coming in drunk on consecutive days, so that could be two or three reds in a row, which would increase the immediate chance of getting caught, but in the long term it would decrease it (which i guess balances out?)

i think I'm getting carried away here because it's Friday morning and I'm full of caffeine, but, with the 'balls test' (in this case) surely the correct way to conduct it, is for two people to be involved, one (the 'drunk', chooses a ball from the bag, and keeps it to them selves, unless the other person (the 'tester') asks them what it is, repeat until either the bag is empty or the 'drunk' gets caught.

#### I'm never drunk...

...just relaxed.

A/C because I am at worked and have just entered a state of private relaxation privately in a meeting room with three stiff G&Ts.

#### No testing required

The probability of me being drunk tonight after I finish my fear, frustration, disgust, and despair-inducing day at work today approaches 100%. (I also have a funeral to go to today)

At work? Nah. I like to be sober during the day just to mix things up a bit. Unless you count our company picnic..

Yes, I was advised to use this approach when calculating the chance of two people in a room of twenty sharing a birthday. It's almost impossible (well, lot's of increasingly tedious fractions) to calculate the chance of it happening, but the chance of it not happening is a lot easier.

#### It's always 50%

The chance of anything happening - being caught on a given day or not - is that it will either happen, or it won't. Some might say that's 50:50, or 50%. These people are known as dicks.

It's easy spotting the drunk at work, it's the one stuck in the photocopier who's had a nasty accident and waiting for the paramedics to attend after a foolish attempt to make copies of their privates.

Alcohol, never touch the stuff as I can't afford both a drink problem and a coke problem. Mind you I could always ask the boss for a pay rise, they're a piss can so might be sympathetic.

#### Too many numbers

It is pub o'clock

Out of here

This post has been deleted by its author

#### The real probability

I was recently faced with the prospect of signing a contract that insisted I take part in the company's testing policy, even though I work for myself.

No amount of negotiating got them to budge, and I was on the verge of rejecting the contract (out of principle you understand) when I decided to read the full policy in detail.

Turns out the selection process is based on

1. Location

2. A list of the people signed in using their access card that morning at that location

3. A random selection of the people from the list.

Since I work remotely, and when I do go to the main office I have to sign in as a guest (I have no access card) there is no chance of me appearing on the list in #2, so probability of being tested = 0.

So I signed the contract :)

#### Plan

So....If I wait until I've been tested and then get very, very, drunk, what are the chances of me being caught the next day??

1: I'm drunk now. 3 pints of 4.5% real ale at lunchtime.

2: Yes I do appear to be a lightweight but I could drink a lot more if I wanted.

3: But only if I eat more than a piece of toast for breakfast.

4: I think I'll have pie and chips for tea.

5: That's northern tea at 6pm not the confused southern 'tea' which is actually dinner. Or lunch. Brunch?

6: What was the question again?

7: Hang on ! I don't even have a job! I could be rat-arsed anytime I want!!!

#### You're all missing the point!

Who is this company and how can we ridicule them?

#### 0.90 vs 90%

My guess is that they've correctly calculated that the probability is 0.90, and then just written 0.90% without multiplying by 100.

#### Simple logic

We cannot know what logic allowed the producers of the table to arrive at the incorrect value of 0.9 per cent

Here's the logic: the producers of the table are marketers who know fuck all about probability but plenty about how to persuade companies to sign up for the highly-profitable daily testing regime.

I ran it using my calculations and got the following:

Test once per year - 4.62%

Test twice per year - 9.02%

Test every month - 43.28%

Test every week - 91.43%

Test every day - 99.9995%

The assumption I made is that every day, there is a 12/260 probability that they will go in drunk, and that each day, the probability of going in drunk is not determined by how many times they have gone in drunk so far in the year, so there is a very small chance that they might go a whole year without getting drunk.

#### Discrete verses continuous

"The assumption I made is that every day, there is a 12/260 probability that they will go in drunk, and that each day, the probability of going in drunk is not determined by how many times they have gone in drunk so far in the year, so there is a very small chance that they might go a whole year without getting drunk."

This has been answered above, it's the difference between continuous probability (as you used) and discrete probability, which is what the assumptions given in the article.

You are also correct that continuous is, for most practical purposes, a better model. But you pick your model based on other needs. The answers are also pretty much the same, apart from daily being 1 rather than almost 1 :)

The assumptions are that the worker is drunk, is testable as drunk, etc for exactly 12 out of 260 days each year. If they have been drunk at work for 12 days, they stop turning up at work drunk.

#### As posted above

I *think* the more logical explanation for the numbers is that a couple of marketers have had a whack at it.

So the *method* for the numbers I believe is

1. Correct finite probabilty calculations have been done, as in the article.

2. It's put in a nice table.

3. It's easy to understand, but it doesn't really sell the product anyway more than common sense will

4. This is bad. Lets edit those numbers

5. OK, first off, bollocks to this 0-1 range. Percentage. 1 = 100% = the best. That goes in first

6. Working backwards, 0.94, that rounds to 0.9, whack a percentage in front and we're done. Wait, percentage at the back. 0.94 = 0.9%. Good job my bonus math is better huhuhhuh.

7. OK, 0.43 that rounds to 0.4, thus 0.4%. Bit high, boss wants to push the weekly test kits. Halve it. 0.43 = 0.2%

8. Allright, lets not reinvent the wheel. halve, round down and percentagise those last buggers.

There we go, conveys the correct "sales story" and explains why anyone could come up with those numbers. I feel the author was too charitable in their assessment of where the "figures" came from.

It's data so badly faked it wouldn't fool an accountant. It's almost funny how bad it is at actually selling the product. One hopes that someone got paid a lot of money to say "multiply by 100, put a percentage at the end", in an expensive advertisement for paying attention at school.

See title.

#### Re: If we accept this article as true, then how does the BOFH still have a job?

Easy - he tells the testers he is next to the open window with the unmentioned shoving ram ;)

#### A good stategy

The old Tartars made their battle plans in two stages. First completely drunk at which stage all kind of silly suggestions were made. The next day when they were sobered up they made the real battle plan. It seemed to have served them well.

I was informed by a colleague in Canada, that the company had sensors down at one highly state of the art US site, that was able to detect what you had imbibed\inhaled & to what extent in the past 48 hours before you even swiped into the plants turnstiles.

#### 100 %

Friday afternoon after a pub lunch, you look drunk.

100 % probability you will be tested positive.

#### More efficient method

Flicker fusion challenge via random phone selection (at 1+ hour from start time).

Non discriminatory, if someone is tired, drunk, has severe 'flu etc they are politely asked not come in until better.

Also helps reduce incidences of people crashing their cars due to working three jobs or ridiculous hours (it happens!) and everyone benefits.

I did wonder if the adding of IR thermometers to phones might reduce seasonal illnesses as a temperature is often an early sign of influenza and Norwalk aka winter vomiting bug.

#### But what day is the testing?

Are we assuming that the weekly test is the same day of the week, or evenly distributed throughout the year?

Does the person come in drunk on a Monday only or are they an alcoholic that comes in drunk 4 days a week (ie Mon-Thu) 3 times a year? If the testing is every Friday neither will get caught.

There's not enough data to give an accurate result.

Says the guy who has just drunk two glasses of prosecco at work (with permission!) and it's gone to his head.

John

Quite a few of us used to go in to work quite drunk (we had a a bar on site), straight after lunch (did I mention the bar on site? (50p per pint!!!)). Alas it got to a point (not surprisingly), that some (myself included) were far beyond drunk and into holy shit, he's completely pissed!!! territory (work from home now, and pace myself (I'm an old git now)).

Not something I'm proud of, but testing wouldn't have helped (I did mention the bar on site, right? (disappeared not long after myself and a few others were fired for being shitfaced after lunch, from what I heard (not surprisingly))), limiting how much the bar would sell you, or a strict "look you can have have this much as the on-site or off-site bar", would've) - yes, I was young and stupid - weren't we all?

## POST COMMENT House rules

Not a member of The Register? Create a new account here.