A classical example that's given for probability exercises is coin flipping. Generally it is accepted that there are two possible outcomes which are heads or tails. However, it is possible in the real world for a coin to also fall on its side which makes a third event ( $P(\text{side}) = 1 - P(\text{heads}) - P(\text{tails})$ ?). How would a mathematician go about calculating the probability of that? Could it be done by simply using respective surface areas or would a proper model be more complex?
Calculating the probability of a coin falling on its side
8
$\begingroup$
probability
physics
polyhedra
-
7sounds more like a physics problem to me, since you are talking not about the side that is first to touch the ground (maybe you are), but the side that the coin will remain on? This makes it less of a prob-based-on-area problem. But if you were to ask about probability of a certain area touching the ground first, you would need to define the width of a coin, e.g. by 'fair' coin would you mean that it's so wide that it can touch with either of 3 sides with equal prob? Then there is a question of what about the edge between the third and either of the other sides? In limit, you talk of a sphere. – 2011-10-03
-
0And in general the part of a coin to touch the ground first is almost always the _real_ edge between one of the faces and the cylindrical surface we usually call the "edge". So that won't help. – 2011-10-03
-
0happened to me once. just one day after I saw it happen in a movie. what is the probability of that happening? :D – 2011-10-03
-
1This happened to me the other day. well not me, but I was present and witnessed my friend throw a canadian penny at a table, it fell and bounced twice... then landed on its side. After long serious debate, we were wondering what the odds of this happening would be, since none of us had ever witnessed this phenomenon before. – 2013-04-11
-
1I dropped a Canadian 10 cent coin years ago (1.22mm thick), and it bounced and landed standing up on its edge. It must be very unlikely, but unlikelihood does not rule out occurrence. – 2016-08-08