Faulty RCD or coincidence?

I thought they may just switch it out. Perhaps they will turn up with another one. As long as it’s quick and painless I’ll be happy

Birthday paradox sends me down memory lane I read Discrete Maths and it was one of the interview questions. Been far too long since my careless Uni days I guess I can live vicariously through my kids when their turn comes. But I suspect it won’t be any fun hearing (if they offer me more then a grunt by that age) they’re upto the same things I was.

I always say to my wife and fellow parents this is Karmic retribution, everything we did too our parents was just a boomerang on a long arc destined to come back and smack us in the face

But like stats, many people don’t grasp that concept, they only ever remember themselves being perfect little saints as children

frusc said:

I thought they may just switch it out. Perhaps they will turn up with another one. As long as it’s quick and painless I’ll be happy

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Yes, maybe. In fact, although the warranty undoubtedly says that you would have to accept a repair, although I'm no lawyer, I suspect that Consumer Law ("your Statutory Rights") might well say that you could insist on a replacement - on the basis that you had paid for a "brand new product, of 'merchantable quality' ", not for a 'repaired' one.

When my 'brand new' WM was replaced after a few days, I asked the guy who delivered the replacement (and took away the faulty one) what would happen to the one he was taking away - and he said "it will go straight into the skip"!

frusc said:

Birthday paradox sends me down memory lane I read Discrete Maths and it was one of the interview questions. Been far too long since my careless Uni days

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The Birthday Paradox certainly is very counter-intuitive, even to statisticians and mathematicians, albeit not the extent of the "Monty Hall Problem" (in relation to which I have seen eminent Statisticians almost 'come to blows'!)

The maths of getting a precise answer is straightforward enough (albeit tedious if 'done by hand'), but there are some pretty good approximations available - for example, a good approximation (using a Taylor series expansion) for the probability of two people having the same birthday in a group of n people is given by p = 1 - e^(-n²/730) - which gives a probability of 51.6% for n=23 and 99.9% for n=70

It becomes even more counter-intuitive as one 'moves up the scale'. To have >50% probability of 3 people having the same birthday requires a group of only 88 people, and to have a probability >50% of 4 people having same birthday only requires a group of 187. The birthday paradox can easily be generalised to the sort of situation we were discussing, simply by changing the probability of a single event (within the time window of interest, not necessarily 1 day) from "1 in 365" to whatever is appropriate:

frusc said:

I always say to my wife and fellow parents this is Karmic retribution, everything we did too our parents was just a boomerang on a long arc destined to come back and smack us in the face But like stats, many people don’t grasp that concept, they only ever remember themselves being perfect little saints as children

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"Recall bias" at work again

Kind Regards, John

Engineers arrived and diagnosed a faulty heating element. Replaced it and tested the oven. Only took them half an hour, so not too bad.

They said the build date was a few years ago, I guess that’s why it was a store closing clearance item. And most likely sitting in storage moisture had got into the element insulation. If I didn’t have an RCD it would probably have cleared after a few uses. But they tested all the elements and changed it and got the oven up and running again.

Monty hall was another popular entrance interview question. Although English professors use the 3 prisoner/hostage variant.

The birthday paradox is more interesting though. I could wrap my head around Monty Hall, but even most Mathmeticians don’t find compound exponential growth intuitive. Rule of 72 is another one people often can’t grasp.

frusc said:

Monty hall was another popular entrance interview question. Although English professors use the 3 prisoner/hostage variant. The birthday paradox is more interesting though. I could wrap my head around Monty Hall ...

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I'm impressed! When, way back, I first grappled with Monty Hall, I could not 'get my head around' the theoretical approaches, and only managed to convince myself (of the correct answer) when I resorted to simulation!

I hope that 'passing the entrance interview' did not rely on producing the correct Monty Hall answer - since, if that had been the case, they might have turned away people destined to become eminent academics

Kind Regards, John

frusc said:

Engineers arrived and diagnosed a faulty heating element. Replaced it and tested the oven. Only took them half an hour, so not too bad. ... They said the build date was a few years ago, I guess that’s why it was a store closing clearance item. And most likely sitting in storage moisture had got into the element insulation. If I didn’t have an RCD it would probably have cleared after a few uses. But they tested all the elements and changed it and got the oven up and running again.

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Good to hear, and I hope that's the end of the problem. It sounds as if (despite what you thought/assumed) the element was somehow 'involved' even during the boot-up process.

Kind Regards, John

JohnW2 said:

I'm impressed! When, way back, I first grappled with Monty Hall, I could not 'get my head around' the theoretical approaches, and only managed to convince myself (of the correct answer) when I resorted to simulation!

I hope that 'passing the entrance interview' did not rely on producing the correct Monty Hall answer - since, if that had been the case, they might have turned away people destined to become eminent academics

Kind Regards, John

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I’m sure it was just the Maths Professors equivalent of pulling wings of a fly. Taking pleasure in making perspective students squirm after a long year teaching their forerunners

For Monty Hall, I mapped out the permutations and calculated the probabilities. Once I could see the permutations it made sense.

Birthday paradox is more abstract, to my mind atleast

It’s odd because I can visualise some exponential compounding expansions. For example collision theory in cryptography I have less trouble visualising. √n is ~ number required for a 50% chance of a match with n items for example. Which ofcourse is another approximation for the Birthday Paradox.

JohnW2 said:

Good to hear, and I hope that's the end of the problem. It sounds as if (despite what you thought/assumed) the element was somehow 'involved' even during the boot-up process.

Kind Regards, John

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Yep, I queried it with them. And they said it runs a self diagnostic during boot up. So I guess it sends some current through the elements briefly, which was enough to trip the RCD.

frusc said:

I’m sure it was just the Maths Professors equivalent of pulling wings of a fly. Taking pleasure in making perspective students squirm after a long year teaching their forerunners

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Yes, probably, but presumably a plan which will have 'failed' if/when they came across an applicant who was already familiar with the problem'/paradox in question!

frusc said:

For Monty Hall, I mapped out the permutations and calculated the probabilities. Once I could see the permutations it made sense.

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I suppose that's essentially what I did when I eventually 'resorted to simulation', since the maths (and correct mathematical answer) then 'made sense'. However, despite that, I have to say that, even decades on, I still have difficulty in 'getting my head around it', since I find it difficult to 'conceptualise' the situation (non-mathematically) in a manner which does not appear to violate the most basic concepts of probability theory!

frusc said:

Birthday paradox is more abstract, to my mind at least

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I certainly find it more interesting/useful, and it's a bit different (from Monty Hall), since it's really just a matter of 'surprise' ('incredulity'?!) regarding the mathematical provable answer, rather than any apparent 'conceptual violations'.

I find it 'useful' because, just as my introducing it into this thread, it is a concept that can be extended into many real-world situations. If one has three items, each with the same (very small) risk of failure in any week in the next five years, then the probability of them all failing in the same week is very much higher than the "astronomically small probability" that many/most of us would probably initially think was the 'intuitive' answer (as with the birthday paradox).

frusc said:

It’s odd because I can visualise some exponential compounding expansions. For example collision theory in cryptography I have less trouble visualising. √n is ~ number required for a 50% chance of a match with n items for example. Which of course is another approximation for the Birthday Paradox.

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Even mathematicians start life as human beings with intuition, and I'm sure that, in many/most cases such as we are discussing those 'initial intuitions' prove to have been wildly 'off' once one has done, and seen the results of 'the sums'!

Whether in relation to 'doubling up' of grains of sand across the squares of a chess board, or a single bacterium 'doubling' every 20 minutes for 24 hours, I don't think that the 'intuitions' of many people who have not 'done such sums' (or seen the results thereof) will be even remotely expecting the 'astronomical' numbers which result - and, to be topical, I imagine much is the same in terms of many people's understanding (or lack of it) of the evolution of a viral epidemic/pandemic!

Kind Regards, John