Question

show all work. A simple dartboard has three areas… the main board has a radius of 8 inches, there is a circle with a radius of 5 inches, and the bullseye has a radius of 1 inch. What is the probability of a random dart landing inside the bullseye?





Round to the nearest thousandth. (Hint: Use A=pi*r2

Answer 1

area of bullseye/area of entire dartboard

provided that you hit the board and the throw truly is random

Answer 2

i dont understand what you mean?

Answer 3

A probability is the part divided by the whole. The whole dartboard can be represented by the area that it takes up. \[A=\pi r^2\]Since the radius of the whole dartboard is 8, its area is 64*pi square inches. The bullseye is pi square inches because the radius of the bullseye is 1 square inch. This means that the probability of hitting the bullseye is \[\pi/(64\pi)=1/64\]
The amount of space available for the center ring is the area of the center ring MINUS the area of the bullseye (since you can't hit both with one throw). Therefore, you get \[16\pi-\pi=15\pi sq.inches\]as the area. So the area of hitting the center ring is (again) the part divided by the whole, or
\[15\pi/64\pi=15/64\]