What is the probablity that the coin will land on its edge?
Take the presidential 1$ coin with 26.49 mm diameter, 2 mm thickness, and 8.1gms weight. Assume smooth rims and a non-bouncing surface.
How will the probability vary with the height of drop?
If you actually flip it so that it looks like a sfere in the air --> never
If you TRY to let it land on it’s side? Every third try or so?
Getting it to come to rest on it’s side will be quite a lot harder.
Sphere.
[quote=“The_Librarian, post:2, topic:577126”]
If you actually flip it so that it looks like a sfere in the air --> never
If you TRY to let it land on it’s side? Every third try or so?
**Getting it to come to rest on it’s side will be quite a lot harder.[/**QUOTE]
Assume there is no bounce once it hits the surface,and it will stay in same position.
My question is, will the probability be a straight 1/3?
:dubious: It is impossible to provide a theoretical probability. There are too many variables. It’s not like drawing black and white marbles out of a bag. It would have to be determined empirically. You would even have to test a coin empirically just to find out if the chances of heads/tails are truly 50/50, since every coin is weighted differently, has different wear patterns, every person who flips it will do it a little differently, surface it lands on will be different, etc.
Try running a million trials and let us know what you find out. If you do get it to land on the edge, also let us know if you can read minds.
Your assumptions aren’t clear. It is starting to sound like you don’t mean that the coin actually lands on its edge and sticks the landing. Do you mean how often will the coin land such that its edge touches the surface upon landing so that the coin is completely vertical, regardless of the momentum of the coin that will cause this configuration to be unstable?
If you rotate the coin about its horizontal axis, you create a circle of circumference 83.22. The thickness of the coin is 2.0 so the probability of the coin landing vertically is 4.0/83.22 = 0.04807 or about 4.81%. That only indicates the configuration the coin is in when it contacts the surface. If the coin’s vector is exactly vertical (highly unlikely) and there is no bounce (damn near impossible) and there is no rotational momentum (impossible if you actually “flip” the coin, by definition), then that is the probability of landing on edge. Height of drop has no effect give your assumptions.
Exceedingly unlikely, perhaps. But never?
I know the OP was asking about a different, more hypothetical “first assume you have a spherical cow” scenario, but seriously, in real life, if you flipped a coin in what would seem to be the “standard” way (so that the coin rotates along an axis running through the coin’s diameter), wouldn’t there be a non-zero probability of the coin landing on a tabletop, say, bouncing and doing whatever gyrations a flipped coin would normally do, and still land and come to rest on edge?
Would the slightly lighter gravity at the equator make a difference? Can’t you do weird things there like stand an egg on its end?
No. Merely because there are three outcomes (heads, tails, edge) that doesn’t mean that each outcome is equally likely.
There is a tiny, tiny probability that a flipped coin will land on its edge. The exact value will depend on such on a large number of real-world parameters that it is virtually impossible to calculate directly. It is non-zero, but for all practical purposes it might as well be zero.
If you’re in a Batman comic starring Two-Face the probabilities approach 100%.
I seem to recall a Twilight Zone episode that started this way.
While flipping a coin to determine who tees off first in a golf match, I have flipped a coin several times and had it land on the edge.
Of course the coin is landing in grass that can support a coin from both sides when that happens.
That doesn’t sound like a reasonable assumption. Taken literally, it means that if it landed even one degree from perfectly flat, it would remain suspended “on edge” at an angle that defies gravity.
I guess if you were flipping a heavy coin over some very sticky mud, you could get it to stick on edge at angles around 45 degrees and above, which would probably happen at least half the time.
I think I remember that story from a million years ago. BM is so deft that he can, with gloves on, in the middle of a fight, pick Two-Faces’ pocket and swap Two-Faces’ deciding coin with one that BM rigged to end up standing on edge after being flipped. I rolled my adolescent eyes. 
Well, he was prepared.
But, seriously, isn’t in the middle of a fight the best time to try to pick someone’s pocket? That’s why pickpockets often bump into you. You’re way less likely to notice it when there’s some bigger physical jolt occurring.
I did once see a coin flip come up “edge”. It hit the floor on edge, rolled, and stopped when it hit the wall, still on edge. IIRC, it was a nickel, the (American) coin with the smallest ratio of diameter to thickness.
So, let’s simplify things. Let’s take a coin as being a metal cylinder x mm in diameter, and y mm thick. With real-life coins, y is much smaller than x, but let’s take “coins” out of that real-life range. With a coin 2 mm in diameter and 20 mm long, you would expect it to land almost always on its edge. With x and y close, say both being 10 mm, you would expect non-zero probability of land on each face and on the edge, and you might also expect the probability to vary depending on how the coin is spun, how far it falls, and how much it bounces when hitting the floor. So it would make sense to do some practical testing of coins of various sizes, and find out how thick they must be for a non-zero chance of landing on its edge.
No. That’s a myth used to suck in tourists in Africa and South America.
Gravity is only about half of one percent weaker at the equator than at the poles.
From practical experiments, with typical materials for the “coin” and the surface it’s landing on, I think it works out that a tuna can is about right for having a 1/3 chance of landing on edge. If you just want a nonzero chance, of course, then any dimensions at all will work.