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

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.

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 did (450-200)/200

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.

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%"

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.

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.

Switch! Switch! The other door has gone from 1/1000000 to 999999/1000000, while yours is still at 1/1000000!

I don't think that has anything to do with this question - which is straightforward and unambiguous. I think it's because many advanced mathematicians aren't actually that good at simple maths. I got stuck behind one of my maths professors at a uni shop one day - the guy had all sorts of awards for problems he'd solved but he couldn't work out how much he needed to pay or confirm the change.

I love the Monty Hall problem

Imagine there are a million doors. I know the door that the prize is behind.
You pick a door.
I then open the doors - and every time I open a door, there is no prize behind. So after opening all the other doors, we are left with 2 doors.

The door you picked at the start.
Or the other door that I haven't opened yet

There are also 999.998 other open doors with no prize behind. Just lots of goats.

Do you swap doors - or do you stick with your first choice?

Or does it make no difference?

Ah yes, that works.

As with the Monty Hall Problem, there is a simple, correct answer that people, including experts, get wrong. This is independent from the missing answer in the button list, which is a separate conundrum. If the question itself is unambiguous yet so many mathematicians earnestly explain why it's 225% or somesuch, how is that not a viridical paradox?

Yeah, so they launch on the first day of year 1 with 10k, by the end of the year they reach 20k.

That would be the first day of Year 1 though, wouldn't it?

To be fair, it doesn't, just my logic that the first day of a newspaper in circulation is when they put some copies out on the street.

Where does it say that ?

Ah, but a new newspaper doesn't start with 0 copies, on the first day they've got to put some out.

Not just me, then! (Not that that means a lot on this thread...)

To be clear, I'm not suggesting that's what the question means as it wouldn't make sense, but there is a potential ambiguity there.

I know it doesn't state explicitly that we are starting at zero. But if it's the first year of circulation [of a newspaper] then it's implicit that we are starting at zero as if it was already being circulated it wouldn't be the first year of circulation.

The "first year" of anything implies nothing has gone before it (although I suppose the year 1AD would be an exception...).

Well the actual question posed is, "What was the percentage increase in circulation of News Today from the end of the first year to the end of the third?"

So it kinda does, or at least could justifiably be interpreted that way imo.

It doesn't say that we are starting at zero.

It could be looking at a normal newspaper that has been around for many years.
Then in 1 year, the circulation doubled. etc

The question says, "In one year the circulation of News Today doubled." But this year can't be "the first year" of circulation, otherwise you're doubling zero.

It never claimed to be the first year of circulation though.

Oh I spent quite a while today thinking exactly that!