back to article 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 …

          1. Arthur the cat Silver badge

            Re: A certain bias, there

            A lot of beers are significantly more than 2 units/pint.

            2 units/pint = 3.52% alcohol. Sessions beers were traditionally ~3%, most beers in my local are above 3.5, some considerably above.

          2. Rich 11

            Re: A certain bias, there

            But serious kudos (and concern for your liver) if you can manage 4 pints of Old Scrooge in an evening!

            Challenge accepted!

          3. Alistair
            Windows

            Re: A certain bias, there

            @Pen-y-gors:

            Five Paddles Mississippi Paddler @ 12.6%. Comes in *quart* bottles. Goes down a complete treat. Mistakenly had a bottle to hand one night whilst tanking -- the last half of the instance was a bit of a blur.

          4. Anonymous Coward
            Anonymous Coward

            Re: A certain bias, there

            A lot of beers are significantly more than 2 units/pint.

            "Snake Venom" from Scotland is supposedly 67.5%, so that's 36 units a pint?

        1. phr0g

          Re: A certain bias, there

          Correct, kind of. But that 8 hours assumes you drank all 4 pints at once.

          units of alcohol is about strength % * volume (in litres)

          So a metric pint (half litre) of 4% beer is 2 units.

          If you begin at at fairly normal 20:00, drink 4 pints between then and 00:00, that's already 2 of the pints gone from the system, the next 2 by 02:00. Driving to work the next day at 08:00 won't be an issue.

          (This is a rough estimate as it takes some time for your liver to start processing the alcohol obv.)

          In the UK, the drink driving limit, roughly, for a 12 stone man, is around 4 units, so you would unlikely be over the limit if you waited an hour or so after midnight and then drove (but I wouldn't recommend risking it).

          1. zappahey

            Re: A certain bias, there

            In the UK, the drink driving limit, roughly, for a 12 stone man, is around 4 units,

            Except for readers in Scotland.

    1. DJ Smiley
      Pint

      Re: A certain bias, there

      It takes me 10 minutes to get to work.

      I could easily down a Pint, come to work, still have it in my system.

      Nothing wrong with a Pint before work at 8am! ;)

      1. Trigonoceps occipitalis

        Re: A certain bias, there

        Always pour the beer the night before, that way it is flat and you can get it down your neck quicker in the morning.

    2. small and stupid

      Re: A certain bias, there

      Why privilege lunch over breakfast?

    3. Pascal Monett Silver badge

      Not a beer drinker, so ..

      Wasn't aware that beer could have that kind of effect.

      So I have to amend my position on alcohol in the morning, since it could simply mean that you had "too much" the night before. I'm okay with that, although I will be encouraging you to drink lots of water during the day.

  1. DavCrav

    The quick way is to do 1-(0.95)^52=0.93 (2 sig figs), which gets you almost exactly the right answer. That's how we were taught to do it in school for continuous events and adding probabilities. The extra accuracy you get by withdrawing balls gives you the correct answer, but the short form above works well, if the testing is still relatively infrequently.

    1. petethebloke

      Agreed. I think there might be other ways of getting the wrong answers in the table (from those suggested in the article) - they don't even follow a progression, which is odd. Monthly is the same as annual.

    2. felixk

      @DavCrav:

      > The quick way is to do 1-(0.95)^52=0.93 (2 sig figs),

      > which gets you almost exactly the right answer.

      No, it gets you exactly the right answer. The use of a hypergeometric distribution is technically correct (but only if the sot keeps track of how many times he's been drunk and stops after twelve such days); personally, I would apply a binomial distribution with a fixed probability of drunkenness on any one day of p=12/260, just as you did.

      The results are: P(X>=1) = 0.935646978954 for the hypergeometric case, P(X>=1) = 0.914321213168 for the binomial distribution. The commenter that decided that the result must round to 0.90 is living in a state of sin.

      1. DavCrav

        "No, it gets you exactly the right answer."

        It gets you the right answer, but to a different question. It gets you the right answer to the question "what is the chance of getting caught given that each day has a fixed probability of you being drunk", whereas the question was that in a given year there are exactly twelve drunk days, so it becomes a finite problem which needs finite methods rather than a continuous probability.

    3. AJames

      "Correct" method is slightly wrong

      I think your rough calculation is actually closer to correct, while the one given in the article is slightly wrong. This is not a case of "removing one ball from the bag" each time as the writer has assumed. In actuality it is likely that the probability of the employee being drunk on any given day is always 12/260, independent of any previous day. In other words, the employee decides on any given day "do I need a drink today?" depending on his or her current circumstances, and is not thinking "wait, I've already gone in to work drunk 5 times this year, so maybe not today.".

  2. Anonymous Coward
    Anonymous Coward

    Counterproductive..

    If I were sober I wouldn't turn up.

    1. Sir Runcible Spoon
      Pint

      Re: Counterproductive..

      What wash the question again?

  3. Amorous Cowherder

    I think we accidentally get hung up on the pertinent request, "If I do something X times, what are the facts about X?". In this case we get caught up on getting to that magic fact being driven by the 52 times/year, the 4 times/year or twice a year and start from there. Just human nature I suppose to look for the quickest route through a problem rather than the correct logical route.

    The "bag of marbles" visual idea for probabilities takes me back to my school days and later on working through maths homework with my own kids. It's such a great little visual image that immediately registers with the imagination. Don't try to imagine an abstract idea of 12 days over 260 because you cannot be two mutually exclusive things at the same time ( drunk and sober ) , but imagine it's ( 260 = 12 + 248 ) , 12 red marbles and 248 green marbles. Immediately most people, even those who really struggle with maths, can visualise instantly and start to get a handle on probabilities. Oddly my imagined bag of marbles is always dark grey felt with a black draw cord, ha ha!!

    1. MrBanana

      It was always different coloured socks in a drawer for me.

      1. Bill Gray

        Socks in a drawer

        I've long tended to grab two socks from the drawer in the morning without really checking to see if they match. SWMBO objected to this behavior. I caved in (always a good idea on minor issues; choose one's battles carefully, etc.) and have since taken a moment or two to ensure a match. But I did explain to her that my previous behavior was just in memory of (seemingly countless) probability problems as a lad such as:

        Eddie has five red socks, three black socks, and two white socks. If Eddie grabs two socks in the morning at random, what's the probability that he'll grab two socks that match?

        1. Richard 12 Silver badge

          Re: Socks in a drawer

          After a few days, zero.

          Socks ever match once they've been washed a few times.

        2. MJI Silver badge

          Re: Socks in a drawer

          Mine is 100% because they are paired.

          2 sets of 7 pairs of day socks

          1 pair of Minion

          A few colourful pairs.

          Thick comfy socks.

  4. jake Silver badge

    Let's be real here.

    If one of my employees shows up obviously under the influence, I'll show them the door. It's that simple, and they know it. They have the option of taking a blood test immediately after being fired, and I'll deal with the consequences if I'm wrong. Thankfully I have never needed to resort to this ... But that's not to say I'll fire 'em if they have booze on their breath. I operate a small brewery, winery, and fledgling distillery. Almost all of my employees have access to, and in some cases are required to sample the product ... Either you trust your employees, or you don't. If you don't, get rid of them. Makes life much easier all around.

    1. Buzzword

      Re: Let's be real here.

      It's not always obvious though. Can you tell the difference between someone who is still drunk from the night before, and someone who has a cold? What if they simply haven't slept properly because of external factors (heat wave, noisy neighbours, etc.)?

      1. jake Silver badge

        Re: Let's be real here.

        Buzzword, I'm fairly certain I can tell the difference. My velcro-whippet certainly can. I'll make the call if/when. And as I said, if I'm wrong I'll face the consequences.

        Hasn't happened yet. Somehow, I doubt it will ever be an issue. Not with this crew; they've all been with me for nearly two decades, and all have a piece of the holding company.

        1. DJ Smiley

          Re: Let's be real here.

          Ok but what if they show up exhausted, because they have kids and they were up all night screaming?

          My point is, that the effect on their work from exhaustion is the same as that of being drunk.

          1. jake Silver badge

            Re: Let's be real here.

            DJ, no it's not. I can tell the difference. So can my velcro-whippet.

            As I said, I'll face the consequences if it ever happens. I'm cool with that.

            1. frank ly

              @jake Re: Let's be real here.

              Does your velcro-whippet stick to them if they're alcohol impaired?

      2. Anonymous Coward
        Anonymous Coward

        Re: Let's be real here.

        Can you tell the difference between someone who is still drunk from the night before, and someone who has a cold? What if they simply haven't slept properly because of external factors (heat wave, noisy neighbours, etc.)?

        Yes, because of the smell of ethanol coming from their skin pores.

    2. DavCrav

      Re: Let's be real here.

      "If one of my employees shows up obviously under the influence, I'll show them the door. It's that simple, and they know it. They have the option of taking a blood test immediately after being fired, and I'll deal with the consequences if I'm wrong."

      If you are in the lovely US in one of those at will states then fine, but in the UK you would be in court pretty quickly with that kind of approach.

      1. Anonymous Coward
        Anonymous Coward

        Re: Let's be real here.

        I want to know what the odds are of someone saying 'Velcro-Whippet' twice in one thread...

    3. MrBanana

      Re: Let's be real here.

      Instant dismissal isn't really necessary. When coming back from a liquid lunch, and having been judged to have forgotten how to count above two pints, my manager would meet me at the office door and offer me a pen and an instant, one day, holiday request form. Then off home. It was usually worth it. Fighting in the car park optional.

      1. werdsmith Silver badge

        Re: Let's be real here.

        I've been at places where when we know we are doing a lunchtime celebration then the network access is revoked in advance. I've also been on lunch celebrations where the boss decided it would be better for people to go straight home from the pub rather than be let loose on the IT systems.

      2. Anonymous Coward
        Anonymous Coward

        Re: Let's be real here.

        my manager would meet me at the office door and offer me a pen and an instant, one day, holiday request form. Then off home. It was usually worth it. Fighting in the car park optional.

        Shrewd manager. He gets half a day of work for you for free!

  5. Anonymous Coward
    Anonymous Coward

    Team goes out on first wednesday night of each month for a "team building exercise" in local pubs/clubs and employees come in drunk ont the day after every month. Company does weekly alcohol screening on tuesdays. Probability of being caught 0%.

    1. Anonymous Coward
      Anonymous Coward

      Ha, we have a rule for company lunches that you can only drink if your manager is present to approve the expense (even if we are paying.) Which often means he can't drink as his manager isn't present. So he drives. it's win-win.

  6. Anonymous Coward
    Anonymous Coward

    It's a version of the birthdays question.

    How many people do you have to have in a room before there is a greater than 1 in 2 chance that 2 of them have the same birthday?

    People tend to guess a number around 183, but the same logic as the drunk testing applies and the answer is in the low 20s. (It is not exactly as calculated because there tend to be more births at certain times of year.)

    1. Andrew Moore

      Re: It's a version of the birthdays question.

      23- it's based on the total number of pairs there are in the room.

      1. katrinab Silver badge

        Re: It's a version of the birthdays question.

        If birthdays are evenly distributed throughout the year. In the UK, 26th September is the most common birthday, and that is the most likely birth date from a Christmas session.

        1. TRT Silver badge

          Re: most likely birth date from a Christmas session

          Ah. Christmas comes but once a year.

          1. Anonymous Coward
            Anonymous Coward

            Re: most likely birth date from a Christmas session

            and clearly so do a lot of fathers..

            I am of course referring to Father Christmas - your minds....!

            1. Anonymous Coward
              Anonymous Coward

              Re: most likely birth date from a Christmas session

              But when he does, he fills your stockings to overflowing.

  7. HmmmYes

    Hmm. Overthinking it a bit.

    My one and only experience of a drunk at work goes back to my first job in the early 90s.

    The 'drink because my wife and kids have left me because I moved the family from <somewhere nice> to Bracknell' rolled in at 3pm, fell asleep, then stood up and peed in his top desk drawer.

    Sitewide no boozing at work policy the next week.

    1. Pen-y-gors

      Drunk and sleeping at desk - sad.

      Peeing in desk drawer - Class!

      1. Little Mouse

        A clearly-defined keyboard imprint in your forehead is not an easy look to carry off at work.

        <cough!> Apparently.

        1. Sir Runcible Spoon

          Round our way we call that qwerty-face

          1. electricmonk

            Shouldn't that be ytrewq-face?

    2. Mark York 3 Silver badge
      Pint

      "The 'drink because my wife and kids have left me because I moved the family from <somewhere nice> to Bracknell'"

      Bracknell = RACAL perchance.

      "rolled in at 3pm, fell asleep, then stood up and peed in his top desk drawer." = https://www.youtube.com/watch?v=oNFz0hkPXvA

      There was a similar sort of Christmas party at RACAL Seaton (Before I joined), there was sex under benches & all sorts of celebrations on return from the pub\in house supplied booze, following year Management wizened up & no such celebrations took place, they just kicked us out at lunchtime & we went straight to The George instead.

  8. Anonymous Coward
    Anonymous Coward

    Idiots

    We know they test once a week. Wait sober until they test, and drink until the weekend. Probability of being caught 0!

    Alternatively, it's almost certain that the boss will have been seduced by sales spiel into buying the latest fanciest internet connected alcohol testing machine. Even the greenest PFY should be able to insert the 'if dept = IT then alcohol = random number between totally sober and reasonably sober' into the code. Or maybe the simpler 'if dept = HR then alcohol = embarrassingly pissed'

    And pedantically, assuming that the employee's drinking is reasonably spread your green and red balls are a bit skewed - (I think - of course last night's bender might be clouding my judgement), because while in week 1 you may have 248 red 12 green, but week 2 we should be calculating 243 red 11.75 green, - the odds of being caught aren't changing any more than the odds of throwing a coin change? Your numbers assume that if I was sober on test 1 the chances of me being sober on test 2 are slightly less, effectively assuming that there are still 12 drunk balls, but now 247 sober ones.

    I think it was just a poorly labelled table and the best way of thinking about it is there's a 12/260 chance that I'm drunk on a given day and a 52/260 chance that I will be tested on a given day

    so for a given day the probability of getting away with it = 0.04 * 0.2 = 0.009 as it was in the table

    They just forgot that I come to work 260 days a year (for which I'd need to be on something) so

    260*0.009 = 2.4, a 240% chance of being busted. That empirically feels right, If I do something where i have a 20% chance of being caught 12 times in a row, I'm going to get caught.

    1. Anonymous Coward
      Anonymous Coward

      Re: Idiots

      What this of course proves, is that there are lies, damned lies, and statistics.

      If the question is not specific, or is open to interpretation almost anything can be proved...

      This is indeed how politicians justify their random meanderings...

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