Coin Landing on EdgeDate: 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/ |
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