What are the chances of tossing a coin standing up?

First of all, from landing to standing, what is the area of the upright part of the coin?

Let the diameter of the coin be 2 cm,

The area of the upright part is about = 0.2 * 2 п = 0.4 п. Coin surface area = 2 п+0.2 * 2 п = 2.4 п

The area of the upright part accounts for 0.4/2.4 = 1/6 of the coin area.

This is the landing probability of the upright part = 1/6.

But landing doesn't mean you can stay put. When the upright part touches the ground, the center of gravity is just perpendicular to the ground, and there is no angular deviation.

Angle deviation probability =1180 (only one semicircle is vertical)

Total probability of standing upright =11080 (this is the probability when the ground is absolutely horizontal, so there is no way to calculate it if it is uneven).