Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Is the Probability of Tossing a Coin Really 50-50%?

Version 1 : Received: 30 April 2022 / Approved: 6 May 2022 / Online: 6 May 2022 (09:03:42 CEST)

How to cite: Pletser, V. Is the Probability of Tossing a Coin Really 50-50%?. Preprints 2022, 2022050064 (doi: 10.20944/preprints202205.0064.v1). Pletser, V. Is the Probability of Tossing a Coin Really 50-50%?. Preprints 2022, 2022050064 (doi: 10.20944/preprints202205.0064.v1).

Abstract

Considering that a fair coin has two sides and a cylindrical edge, the probability that it would fall on its edge is calculated, yielding the probability of heads or tails less than 50%. Theoretical models for a static case and for five dynamic cases, without and with rebounds, show that there is a small probability that the coin does not fall on its head or tail, depending on initial toss conditions, the coin geometry and conditions of the coin and landing surfaces. For the dynamic model with rebounds, it is found that the probability that a 50 Eurocent coin thrown from a normal height with common initial velocity conditions and appropriate surface conditions will end up on its edge is in the order of one against several thousand.

Keywords

coin toss; probability; impact

Subject

MATHEMATICS & COMPUTER SCIENCE, Probability and Statistics

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