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### Coin Landing on Edge

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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
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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

- Doctor Shawn, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Probability

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