Is My Masterplug RCD Safe? Please Help!

[JohnW2]

[in response to EFLI]I fear you have missed the 'issue' The countless thousands (or millions) of (wo)man-hours that have gone into the discussions, debates and arguments over the years about the MH problem have all been about the probability of winning if one switches (or doesn't switch). In other words, "If it is accepted that it is two thirds when switching..." is very far from 'being accepted' without a big fight!!

The Wikipedia gives a nice brief summary which hopefully will convince you (EFLI) that the 'two-thirds when switching' probability has been far from readily/easily 'accepted':

Vos Savant's response was that the contestant should switch to the other door. (vos Savant 1990a) ... Contestants who switch have a 2/3 chance of winning the car, while contestants who stick have only a 1/3 chance. ... Many readers of vos Savant's column refused to believe switching is beneficial despite her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos Savant was wrong (Tierney 1991). Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy (vos Savant 1991a). Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation confirming the predicted result (Vazsonyi 1999).

Kind Regards, John

 

[EFLImpudence]

I haven't studied it but have seen it explained on television.

However, as far as the 'non switching' probability is concerned it is obviously one in three as that is the choice that was made - three doors, one choice.

When not switching, the fact that a goat is revealed after the event is irrelevant as that was and is always going to happen and that was known before the choice was made.

It is like saying pick any one of three and before revealing whether the correct choice was made a wrong one will be shown.
What difference can that make to the odds when choosing?

Just as well do a 'Bull'seye' and reveal the winner's choice first and then "let's have a look at what you could have won".
It changes nothing.

 

[JohnW2]

However, as far as the 'non switching' probability is concerned it is obviously one in three as that is the choice that was made - three doors, one choice.

That's obviously the probability at the time the choice was made. All the discussion/argument has been about whether the probability of the car being behind that door remains unchanged despite 'subsequent events'.

It is clearly not a general truth that probability of the first door winning is always going to remain unchanged regardless of any 'subsequent events'. Consider the rules of the game changing such that the presenter opened one of the two remaining doors at random. If he chose the one with the car, the probability of the contestant's door having the car (which was a one-third probability at the time the initial choice was made) would then. at that point in time, obviously be zero (regardless of whether the contestant switched).

Kind Regards, John

 

[EFLImpudence]

However, as far as the 'non switching' probability is concerned it is obviously one in three as that is the choice that was made - three doors, one choice.

That's obviously the probability at the time the choice was made.

What else is there?

All the discussion/argument has been about whether the probability of the car being behind that door remains unchanged despite 'subsequent events'.

How can anything have changed it?

It is clearly not a general truth that probability of the first door winning is always going to remain unchanged regardless of any 'subsequent events'.

It is still the same as when the choice was made.

Consider the rules of the game changing such that the presenter opened one of the two remaining doors at random. If he chose the one with the car, the probability of the contestant's door having the car (which was a one-third probability at the time the initial choice was made) would then. at that point in time, obviously be zero (regardless of whether the contestant switched).

Well, of course it would.

i.e. you have won 0% or 100% of your game(s).

The probability would change if the rules were altered to have three cars.

 

[JohnW2]

Consider the rules of the game changing such that the presenter opened one of the two remaining doors at random. If he chose the one with the car, the probability of the contestant's door having the car (which was a one-third probability at the time the initial choice was made) would then. at that point in time, obviously be zero (regardless of whether the contestant switched).

... Well, of course it would. ... The probability would change if the rules were altered to have three cars.

Perhaps I'm not being clear enough. Yes, of course, different games will have different probabilities, but I'm talking about changes (or the absence of them) in probabilities during the course of a game.

As I've said, if everyone had been happy that the initial probability could never change, the whole thing would have been totally trivial and we would not have had these thousands of people arguing about it over the years.

To my mind, there is an extremely simple way of 'proving' the correct answer (essentially not far from some of the things you have said), but that doesn't seem to have prevented all the debate and disagreement over the years!

Kind Regards, John

 

[skotl]

In all the years that internet forums have been in place, I'd be surprised if any thread has strayed so far away from the original topic

But I'm enjoying it, so don't let me stop you

 

[EFLImpudence]

but that doesn't seem to have prevented all the debate and disagreement over the years!

That is what some people do when and because it is their job.

Next motion at Council meeting -
"That the people don't need us any longer".

 

[ban-all-sheds]

[This is obviously all a bit difficult for me, since I 'know the answers' and am trying to represent (at Devil's Advocate, one might say) the difficulties and counter-arguments which many people come up with.]

It's also difficult for me, because I was one of those, who when first presented with the puzzle, was absolutely certain that it could not possibly make any difference if you switched, because there were 2 doors left, and 1 goat and 1 car left (or in my case, one hollow chocolate rabbit worth £5 and one solid gold rabbit worth £50,000).

I think that one of the problems which 'they' have with what you say above is they find it hard to accept that, even though you've put the "1 in 3 chance of a car, 2 in 3 chance of a goat" label on their first-choice door, that those probabilities remain unchanged once one of the three original options has been taken out of the equation.

But what has changed? Unless you postulate somebody moving goats and cars around behind the scenes, what is behind each door after the reveal is the same as before, therefore if your chosen door was originally 1/3 car - 2/3 goat it cannot have changed.

Actually I quite like goats - not saying I'd rather win one than a car, but I've sometimes thought that if I were to keep animals, goats would be a likely choice - I like their attitude.

 

[JohnW2]

but that doesn't seem to have prevented all the debate and disagreement over the years!

That is what some people do when and because it is their job.

I think you seriously underestimate how much controversy and passionate difference of 'expert opinion' there was about this. There was a time when one couldn't go to any (national or international) conference of mathematicians or statisticians without finding huddles of people in every bar, restaurant, coffee room or 'any corner of the foyer they could find', passionately arguing about this issue - and, of course, once 'the Internet' appeared and it got out to the masses, probably literally millions of people (most of who had totally unrelated 'jobs') got involved in equally heated discussions about this.

There is an incredible amount about this on-line, and there are also many 'related' topics. If you ever have the time, you might be interested in reading the whole of the (pretty long) Wikipedia article, which gives a fair insight into the extent of the 'contrtoversy'.

Kind Regards, John

 

[ban-all-sheds]

But what if you had a large conveyor belt, and you put an aeroplane on it, and ran the conveyor belt backwards to match the speed of the aircraft's wheels, would the plane take off?

 

[JohnW2]

In all the years that internet forums have been in place, I'd be surprised if any thread has strayed so far away from the original topic But I'm enjoying it, so don't let me stop you

I'm not so sure - I think I've seen bigger 'strays' in my time

... and this one has done it in at least two distinct jumps In fact, it very quickly got off the OP onto questioning why the OP wanted RCD protection. But then ... first onto RCDs in general (despite the title of the topic) and the statistical value of having the protection of one, two or none of them - and then (via an innocent statement from me about people having difficulties in assimilating probabilistic information about electrical risks!) to where we find ourselves now!!

I wanted to shift each of those 'spin-offs' into new threads, but, by the time I realised what was happening, there were really too many 'spun-off' posts already present. If I had the ability to 'split threads', I would have done it (at least twice!) in an instant.

Kind Regards, John

 

[JohnW2]

It's also difficult for me, because I was one of those, who when first presented with the puzzle, was absolutely certain that it could not possibly make any difference if you switched, because there were 2 doors left, and 1 goat and 1 car left (or in my case, one hollow chocolate rabbit worth £5 and one solid gold rabbit worth £50,000).

... in which respect you are in the very good company not only of myself, but also of a very high proportion of people when fisrt presented with the problem, including many with very serious mathematical or statistical brains. In fact, in the earliest days of all this, I saw some quite serious sums of money lost in wagers by some people who were 'absolutely certain' about that incorrect view!

But what has changed? Unless you postulate somebody moving goats and cars around behind the scenes, what is behind each door after the reveal is the same as before, therefore if your chosen door was originally 1/3 car - 2/3 goat it cannot have changed.

Quite - but, as I've been saying to EFLI, the whole thing is incredibly odd, to have generated so much debate, contoversy and passion, from experts and 'lay' people alike, despite the basic simplicity of 'the truth'.

Kind Regards, John

 

[EFLImpudence]

But what if you had a large conveyor belt, and you put an aeroplane on it, and ran the conveyor belt backwards to match the speed of the aircraft's wheels, would the plane take off?

Ah. That depends what you actually mean.

Aircraft don't use their wheels for propulsion so the wheels don't have any rotation of their own - only reacting to the ground/conveyor.

 

[ban-all-sheds]

Try telling that to the people who believe that you could keep the plane stationary by moving the conveyor belt backwards to "compensate" for the forward rotation of the wheels.

 

[ebee]

This post has had a few tangents (Yes I`m guilty as charged).

No one mention "can a fly stop a train?"