Coin Landing on Edge

Date: 11/29/2001 at 21:45:08
From: J Milner
Subject: Coin toss probability EDGES

Yesterday I was helping a student with some probabilty questions. I 
was about to leave the room while she tried some tosses to get some 
raw data and compare to the predicted values. I put two coins in my 
hand, tossed them up, and let them fall to the desk. To make a long 
story short, after bouncing and spinning, one came to rest on its 
edge. I was astounded. I have been talking about it non-stop for a day 
and a half now.

I try to be precise in my classes and have always said while 
TECHNICALLY coins are not 50/50 H/T because they could land on edge, 
this is not a reasonable thing to expect.

Just what were the chances of this happening? A Canadian copper penny, 
round. Anyone know?

I must say... I'm THRILLED there were three of us there. I know I'd 
never believe someone who said they saw this!

J Milner

Date: 11/29/2001 at 22:26:59
From: Doctor Shawn
Subject: Re: Coin toss probability EDGES

J,

If you've ever seen the movie "Mr. Smith Goes to Washington," you'd 
see the same thing used for comic effect.

I don't think that there's any exact answer to your question except to 
say that there is some nonzero but small chance that a coin will land 
on its edge. (I've found a site claiming that the probability of this 
is less than 1 in 2000, but unfortunately they don't show their work.)

  Spinning Coin
  http://www.fortunecity.com/emachines/e11/86/spinning.html   

Also, there's "research" being done on three-sided coins:

  Three-Sided Coins
  http://www.frii.com/~dboll/coin3.htm   

However, these coins are designed with the aim of getting heads, 
tails, and side with equal probability, so that's not really what you 
are looking for.

You're correct in saying that math coins will always land heads or 
tails, though, because they have no edges. They are sitting on the 
shelf next to the massless pulleys by the 100% efficient freezer full 
of frictionless ice, in a perfectly cylindrical room where there is no 
air resistance. All this goes to say, of course, that real-world 
situations are imperfectly modeled by even the best simulations, and 
that anyone who thinks he can predict everything had better keep on 
his toes.

Hope you have a great day!  If you have any other math-related 
questions, we're at your service.

- Doctor Shawn, The Math Forum
  http://mathforum.org/dr.math/