Vagueness and the Aftermath - A sporadic diary

[RED-DOG]

My daughter thought trilogy was pronounced tri-ology.

[RED-DOG]

I don't know why I wonder about these things but I do.

Yesterday during a project I removed 32 screws and then later I replaced them. The screws were identical so I replaced them at random. How many screws are likely to have ended up in the original hole?

[Tal]

I don't know why I wonder about these things but I do.

Yesterday during a project I removed 32 screws and then later I replaced them. The screws were identical so I replaced them at random. How many screws are likely to have ended up in the original hole?

My immediate reaction is the most likely number is one.

Each one has a 1 in 32 chance of being in its original hole and there are 32 of them.

[david3103]

I don't know why I wonder about these things but I do.

Yesterday during a project I removed 32 screws and then later I replaced them. The screws were identical so I replaced them at random. How many screws are likely to have ended up in the original hole?

My immediate reaction is the most likely number is one.

Each one has a 1 in 32 chance of being in its original hole and there are 32 of them.

The first one has a 1 in 32 chance, the second may have a zero chance because it was supposed to go in the hole the first one went in, or it has a 1/31 chance, and so on?

It's all about conditional probability innit.

[RED-DOG]

the second may have a zero chance because it was supposed to go in the hole the first one went in,

This is what I'm talkin' 'bout.

[Doobs]

I don't know why I wonder about these things but I do.

Yesterday during a project I removed 32 screws and then later I replaced them. The screws were identical so I replaced them at random. How many screws are likely to have ended up in the original hole?

My immediate reaction is the most likely number is one.

Each one has a 1 in 32 chance of being in its original hole and there are 32 of them.

The first one has a 1 in 32 chance, the second may have a zero chance because it was supposed to go in the hole the first one went in, or it has a 1/31 chance, and so on?

It's all about conditional probability innit.

0 + 31 x 1/31 = 1?

That doesn't mean that 1 is most likely, just that on average you'll get 1 in the same hole.  I suspect 0 is most likely, but too tired to work it out.

[Tal]

I don't know why I wonder about these things but I do.

Yesterday during a project I removed 32 screws and then later I replaced them. The screws were identical so I replaced them at random. How many screws are likely to have ended up in the original hole?

My immediate reaction is the most likely number is one.

Each one has a 1 in 32 chance of being in its original hole and there are 32 of them.

The first one has a 1 in 32 chance, the second may have a zero chance because it was supposed to go in the hole the first one went in, or it has a 1/31 chance, and so on?

It's all about conditional probability innit.

Hmmm...but we don't know that. It's the same reason the chances of being dealt pocket aces aren't affected by whether you're in the small blind or on the button, isn't it? If you found out after each screw replacement whether it was in the odd hole or whether the next screw's hole were available, that would be different.

FWIW I'm not sure I'm right on this, because my answer means it doesn't matter whether it's 32 screws and holes or 3.2million of each.

Edit: officer Doobs is most likely Da Man.

[Rod Paradise]

I don't know why I wonder about these things but I do.

Yesterday during a project I removed 32 screws and then later I replaced them. The screws were identical so I replaced them at random. How many screws are likely to have ended up in the original hole?

My immediate reaction is the most likely number is one.

Each one has a 1 in 32 chance of being in its original hole and there are 32 of them.

The first one has a 1 in 32 chance, the second may have a zero chance because it was supposed to go in the hole the first one went in, or it has a 1/31 chance, and so on?

It's all about conditional probability innit.

Hmmm...but we don't know that. It's the same reason the chances of being dealt pocket aces aren't affected by whether you're in the small blind or on the button, isn't it? If you found out after each screw replacement whether it was in the odd hole or whether the next screw's hole were available, that would be different.

FWIW I'm not sure I'm right on this, because my answer means it doesn't matter whether it's 32 screws and holes or 3.2million of each.

Edit: officer Doobs is most likely Da Man.

I've tried working it out - and my head hurts.

Set up an Excel table which allocated a random position to screw 1-32 and checks for them getting the same random number as their number in the list. I ran 500 test runs.

356 got none right.
93 got 1
39 got 2
9 got 3
2 got 4
1 got 5.

roughly 1 in 4 has at least one screw in the right hole.

How to prove it mathematically - life's too short....

*Yes I realise I'm saying that after spending half an hour trying to work all this out....

[Jon MW]

off the top of my head 1-(n-1/n)^n seems right, but this margin is too small to prove it  

[Jon MW]

off the top of my head 1-(n-1/n)^n seems right, but this margin is too small to prove it  

Oh no!

I didn't read the question properly - what I've put is obviously the chance of getting any in the right place for n screws and holes.

I'd go with Tal's logic as well; there are 32 chances to get 1/32 so the most likely outcome is 1 (assuming you don't check them one at a time as you go along)

This'll teach me not to try any maths while I'm trying to pretend to work

[RED-DOG]

15 years ago I paid £100 for a very nice comprehensive tool set which was in a half price sale at Halfords. It's served me really well over the years,  I've broken the odd socket or lost the occasional spanner now and then but I've made a point of replacing them straight away to keep the set complete.

Then this morning, horror of horrors, the plastic toolbox hinge snapped causing the toolbox to fall in half and rendering it unusable.

I could have transferred the tools to another box but this box has dedicated cut-out sections for everything, so if a tool is missing or hasn't been put back, it sticks out like a sore thumb. The accusing gape of the empty space staring up at me has helped me to keep the set complete for all these years, if the box goes, it won't be long before the tools start to follow suit.

So I made a special trip to Go Fixings (one of my all time favourite shops) and purchased two metal hinges of precisely the right size, and eight stubby self tapping screws, thick enough to do the job, (I had to ream the hinges a little for them to pass through) but short enough not to pierce the double skin of the box and protrude to the inside.

It turned out great. I'm predicting at least another 15 years use.

Posted for the gratification of Nirvana, who seems to be tittilated by this sort of thing.

Click to see full-size image.

[nirvana]

Haha, I really do. I love the frugality (if that's a word), the skill, the patience, the looking afterness of it all. The box sounds like a good example of 5S disciplines, in it's own small way, that you'll find in any good workshop or manufacturing plant.

I've never been much of a looker after and it's hard to count the skips I've filled over the years with stuff that should have lasted longer or perfectly good junk because I couldn't be bothered to maintain, repair, find a new home for it or a buyer.

So, I think we're just drawn to the things we're not and I love watching things getting done that I've been poor at - in this case it helps offset the negative feelings I have about my own consumerism and inclination to see most things as disposable.

[RED-DOG]

Haha, I really do. I love the frugality (if that's a word), the skill, the patience, the looking afterness of it all. The box sounds like a good example of 5S disciplines, in it's own small way, that you'll find in any good workshop or manufacturing plant.

I've never been much of a looker after and it's hard to count the skips I've filled over the years with stuff that should have lasted longer or perfectly good junk because I couldn't be bothered to maintain, repair, find a new home for it or a buyer.

So, I think we're just drawn to the things we're not and I love watching things getting done that I've been poor at - in this case it helps offset the negative feelings I have about my own consumerism and inclination to see most things as disposable.

I do enjoy doing this sort of stuff but you're right, frugality is the driving force. Well that and the fact that I abhor waste.

I wish I could let myself be a bit more bala sometimes but I just can't.

For example, My brother John and I are planning to do a little European motorcycle tour, we've been planning it for ages. We both needed protective clothing. He went into a motorcycle accessories shop and bought a Jacket ~ £200, Kevlar jeans £100+ Gloves ~£60 etc..

I trawled the charity shops and car boot sales. I got gloves for £3, Trousers for £5, and a leather jacket for £7.

I can't help it. The way I see it, finding those items is equivalent to going out and earning £300. Plus, the leather jacket I bought was all neglected and sad, but I treated it with some saddle soap and TLC and now it has a new lease of life.

John says I'm too busy farting around saving pennies to earn pounds. The worst part is, I know he's right.



This is us on a practice run to Skeggy the other week.

Not long now, God willing....

Click to see full-size image.

 

[RED-DOG]

So, I think we're just drawn to the things we're not

I wish I had been in a band or gone to uni.

[RED-DOG]

I'll tell you who is bala, BobbleHat. He bought me a book once, never asked me for the money or anything...