360” is the cornhole board so is therefore the denominator and the total size of the board.
If the hole has a diameter of 4 inches, we would divide by 2 to get the radius as the radius is 1/2 of the diameter. Once we have the radius (2 inches). We would then find the area of the hole to find the probability of a point being landed inside the hole.
The formula to find the area of a circle is Area = pi • radius squared
So, A = 3.141 • 2 • 2 = 12.564”
The area of the circle is 12.564”
We could then do
12.564” ———— = 0.0349 = 3.49% 360”
This means there is a 3.49% chance of landing a point into the hole. We could subtract 100% by 3.49% and get 96.51% OR
Since we know the area of the hole is 12.564”, we could simply subtract the cornhole board by the area of the hole and then divide that by the cornhole board.
360” - 12.564” = 347.436”
347.436” ————- = 0.9651 = 96.51% 360”
The probability of a point being on the board but not inside of the hole is a 96.51% chance (IF THERE IS NO BIAS VARIABLE MESSING WITH IT AND THERES AN EQUAL CHANCE OF LANDING A POINT).
Let h be the height to which latter of length of 20 ft reach then using Sine formula in right triangle with hypotenuse 20 & vertical leg h & opposite acute angle 0 = 72∘ sin θ =h 20 sin 72∘= h 20
