General Betting
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Something really strange happened to me yesterday, I need to know what the odds or percentage figure is for this happening -
Yesterday I was repairing a door, I needed to cut a piece of board to the following measurements - 21 cms x 86 cms
I measured and marked 21 cms in from the edge of a 1 meter long board in several places along its length
I then used a long straight edge to draw a line through the 21 cm markings, I didn't draw the line all the length of the board - I stopped at a point that I considered to be longer than 86 cms
Now here is the crazy bit - When I placed my tape measure along the line I had drawn to mark off at 86 cms, I was amazed to see that I had drawn my line to EXACTLY 86 cms
The thickness of my pecil line was .333 mm recurring
Please will one of you help me in calculting the chances of this happening
Do I simply divide the 1 meter length of the board by the thickness of my pencil line or is there more to it (as in the 86 cms I needed)
Thank you in advance
Yesterday I was repairing a door, I needed to cut a piece of board to the following measurements - 21 cms x 86 cms
I measured and marked 21 cms in from the edge of a 1 meter long board in several places along its length
I then used a long straight edge to draw a line through the 21 cm markings, I didn't draw the line all the length of the board - I stopped at a point that I considered to be longer than 86 cms
Now here is the crazy bit - When I placed my tape measure along the line I had drawn to mark off at 86 cms, I was amazed to see that I had drawn my line to EXACTLY 86 cms
The thickness of my pecil line was .333 mm recurring
Please will one of you help me in calculting the chances of this happening
Do I simply divide the 1 meter length of the board by the thickness of my pencil line or is there more to it (as in the 86 cms I needed)
Thank you in advance
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Odds of this happening is evens. Percentage figure of this happening is 50.
This is so because there is only two possible outcomes. You either draw the line to exactly 86 cms or you don't. Ignore all other answers...  |
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The odds of you drawing the line to exactly 86 cm is infinity. The odds of you knowing you've drawn it to exactly 86 cm is zero.
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chances of you thinking it is significant or freaky and to look for explaination: 100%
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This can't be answered using maths because you were TRYING to draw a line 86cm long and we don't know anything about how good you are at doing this.
If you really want to estimate how likely this was go and get 30 more doors and go through the same process again 30 times, don't measure the lines until you have done all 30 doors and then report the length of the lines here and we should be able to estimate the chances of what you did. And 30 isn't a magic number... 100 would be better... but probably less practical ;-) |
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The odds won't be the same as initially, because he has now learned the what is required to get to 86 cms by hand.
FYI a pencil line cannot recurr. I measured and marked 21 cms in from the edge of a 1 meter long board in several places along its length How many is several and how were they spaced, because 4 times plus 2 cms is easy to do? I have a feeling you don't realise that subconsciously you set your self up to be exact. One cannot quantify the odds of thought process unless you fill out an 80 page booklet and send it to Sweden. |
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Thank you for the above comments - some of them have helped
I must add that I didn't know the length of the board That I drew my line on (I measured it after the event so as to be able to try and calculate the chance of this happening) - I did know that the board was bigger than the 86 cm gap I was repairing I had totally overlooked the fact that I couldn't possibly draw a line say about half way along the board and think I was close to 86 cms Having given this much thought - I consider myself capable of drawing a line anything from 70 cms to 100 cms time and time again on a random length of board Does the above information help? Thank you in advance |
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The give a fair measure of the probability you have to have a prior distribution of where you will draw the line. You weren't just drawing the line blindly at any point along the door so it's not fair to say that the distribution was uniform (i.e. equally likely to be at any point) so from experience can you make a statement such as "you are generally on target but within 5cm 95% of the time"? You could use this to determine a normal (Gaussian) distribution of how you expect to fare.
The second point raised in the replies is that you can't measure perfectly precisely, so you can estimate how precise your measurement is (say to 1mm) and your probability of hitting 86cm will actually be the probability of being within 1mm of 86cm. If this all sounds a bit woolly to be mathematical then I'm afraid that's because probability is just a measure of uncertainty and you need to be careful to reflect the information available before you drew the line. |
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In answer to -
"How many is several and how were they spaced"? I have made a mistake in using the word several I marked the board 21 cms in at each end and 21 cms in roughly at the center of its length Please help - Thank you in advance |
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Regarding "FYI a pencil line cannot recurr."
The pencil line was .3333333333333333333333333333333333333333mm thick I am led to believe that .333 mm recurring means the same thing |
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alright... I'm going to attempt to give you an answer... this is the kind of answer I would give in an exam or some other situation where you have to work with only what you are given and can't talk back.
We have 1 estimate of mean = 86cm exactly you said you could draw a line 70-100cm 'time and again' - so I'm going to interpret this as six standard deviations (big assumption)... and for convenience I'm going to change it to 71-101cm (so that 86 is right in the middle)... So we end up with one standard deviation being (86-71)/6 = 2.5cm Then we'll assume a normal distribution cos we have nothing better to work with, mean=86cm, standard deviation =2.5cm Your pencil was 0.333mm = 0.0333cm wide, so the range (based on the centre of the pencil) where the line overlaps 86cm was 85.98335cm to 86.01665cm. The area under the normal curve in this range is 0.5314% (188ish to 1) |
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Nice answer Martinch, I was headed down that route but yours is far more thorough!
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Martinch
Thank you very much for your time Having read all the replies I have now come up with my own thoughts on this I will post something later, please check back and dont hesitate to correct my errors if and when you find them Good luck |
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Just to be pedantic...
The pencil line was .3333333333333333333333333333333333333333mm thick A pencil line cannot be that thick, as the size of the impression cast from the thickness of a pencil cannot be quantified that thin, because even with the best sharpener, you cannot get it that precise. Even sharpening it by laser, the thickness would be measured to three or four decimal places at best. |