Maths question - Civil Service is wrong (we now have 100% more threads about the subject)

[Sharingaroomtinightthen]

When I posted late last night I thought I’d get maybe half a dozen replies confirming the question didn’t have the correct answer and advising whether to tell the Civil Service recruiters. But here we are 1000 posts later.

https://www.mumsnet.com/talk/am_i_being_unreasonable/5384347-maths-test-to-think-civil-service-have-it-wrong

There's also the birthday paradox as an example of probabilities flying in the face of intuition. There's 365 days in the year, yet in a group of 60 people there's a higher than 99% chance there will be 2 people sharing a birthday.

People sometimes struggle with the fact that it's not a match with them - but the fact that any 2 people could have a match.

On the other hand, when you realise that if there are 60 people in the room and you wanted to pick just one pair of people, there are 1770 possible pairs, so it then becomes less surprising that there is at least one pair in there who share a birthday.

Actually, it's just occurred to me that I can use a Poisson approximation with that to estimate that the chances of a shared birthday will be around 1 - exp(-1770/365) = 0.992, which agrees with @SoSoLong 's "over 99%"

It could be a VERY clever (sneaky) question that deliberately has no correct option for the answer. It would be especially useful in a timed test - OP doesn't say if the test was timed. If you take too long on the question you could lose marks by not completing the whole test.

If I met this in a test I would NOT tick any of the incorrect boxes (instant mark lost). I would write 125% to the side and MOVE ON.

PS. I should have changed my username to Kobayashi Maru for this post.

I did (450-200)/200

You swap. Used to drive me mad when they didn’t swap on deal or no deal after my maths teacher explained that you should always swap.

Sorry, trying to quote @cakeorwine

It wasn’t timed and you couldn’t write anything on the side.

This doesn't surprise me at all. Errors in exams/tests are pretty common in my experience. Exam setters make mistakes! I work for a prestigious university and the number of errors in our final exams is embarassing really. It's a bit different as the people setting university exams are specialists in their field rather than specialists in exam setting (and will probably see that job as rather a tedious chore, to be honest) whereas the civil service presumably employs specialist test setters for this (but not specialist mathematicians).

I agree that the correct answer is 125% and anything else is way over thinking!

(I also suspect that the intended answer is 225% and that is probably what I would write in an exam as the best chance of getting the mark. These tests will be computer marked, no-one will be reading your notes on the true correct answer or giving you any credit for not entering an answer)

I love the Monty Hall problem. I think I largely owe my Oxford undergraduate place to it. Back in the day when there were written entrance tests I took the "Maths for non-mathematicians" paper and one of the problems was the Monty Hall problem, which I had never come across before and solved perfectly using Bayes rule. I felt very smug when I later learned it was a problem that had caused some mathematicians so many difficulties.

(The rest of the paper was a bit a car crash! It wasn't the kind of paper where you were expected to be able to do everything, but I didn't know that at the time and I came out thinking it was a complete and utter disaster!)

Edited to add: I just checked the dates. Apparently the Monty Hall problem became well known in 1990 after it appeared in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990. I took the entrance exam in 1989 so it was reasonable to belive no candidates would have seen it before.

Are there marks deducted for incorrect answers in the test? Sorry I can't be bothered to read the whole thread to see if it says this somewhere.

If so, then better to skip I guess.

And the Monty Hall Problem is still causing difficulties. Although the solution is settled (it's 'Yes'), the expert view that, for example, the assumption that 'the host never varies their behaviour' is essential is false. It's also arguably 7/12, rather than 2/3.

@BrickBiscuit It is interesting how few difficulties it caused me as a naive 17 year old.

The original question is simple algebra. Nothing to do with Monty Hall,statistics or variable change!

I’m thinking you aren’t the ‘naive thicko’ - I know that isn’t quite an accurate quotation, but it is close, and captures the spirit - that you first described yourself to be. :)

I have repeatedly pointed out that without the candidate guidance, we are at a disadvantage.

One way to move forwards is to invent our own reality, and then answer that - and it's not impossible this is actually what is required. After all it's looking for the ideal candidate for HMRC - never known for fans of reality.

Civil service tests do not require algebra, trust me 🤣

Sometimes these ever so intelligent academics actually have no common sense or reasoning skills and look for complexities that aren’t there. That’s why these tests are designed not just to test for the best mathematician, but the best all round person for the role.

@Team125

It’s YOU! You took the best name ever 🤣

It’s just your bog standard candidate guidance.

https://www.gov.uk/guidance/using-the-civil-service-jobs-website

Thank you, very kind. One thing I am not is a mathematician. I have published peer-reviewed quantitative research, but always employing a statistician. I could not, for example, accept that 0.999... =1 from a notational proof while a thought experiment involving infinitely-divisible particles shows otherwise. This probably disbars me from the field. So, we have two well-posed problems, the MHP and this MCQ. Each gives sufficient information to return a unique solution which varies with the data provided. No further assumptions are necessary. The actual calculations are trivial. Yet knowledgeable people argue passionately for the wrong answer. The paradox in both cases is that the solution is simple, yet counter-intuitive to both novices and experts.

I see the MCQ question working on two levels. First, yes, the correct answer is omitted from the options. Faced with this error, people have to decide how to answer. Second, the actual calculation (which is trivial in its simplicity) is independent of the option set. Many people are doing it wrong. That’s the counter-intuitive bit, and I think that mirrors the MHP quite closely.

What thought experiment is this?

Isn't it 225%?

END of year one say 100.

Trebles to be 300.

Loses one quarter to make 225.

You have a bucket full of a sand-like substance, and an empty bucket. The substance is infinitely divisible, so there is no particle too big to separate. You transfer 90% from the full to the empty bucket, and repeat ad infinitum. Your ‘new’ bucket will contain 0.999… of the substance, but will never be full.

Okay, I am a mere maths orientated STEM PhD but moderately theoretical. I don’t get this. Infinite divisibility is the devil’s handiwork, as anything infinite is technically approached as a limit.

So I may have a hard time with an ‘infinite vibe’. I see that intuitively the first bucket will never empty. I don’t see that you have .999999…….. of the particles in the second?

PS Probably signing off MN now. No disrespect to this tantalising problem