Introduction to Probability

Question

You shoot an arrow at the target shown, whose diameter is 40 inches. The red bull's-eye is 8 inches in diameter. The rings have equal widths. If the arrow is equally likely to hit anywhere on the target, what is the probability it lands in the bull's-eye? ( Hint: Area of a circle is A=π r².)

Answer 1

The diameter of the bulls-eye is 1/5 of the dimeter of the target, thus radius of the bulls-eye is 1/5 of the radius of the target. Since we care about area, not radius or diameter in this case, and area is related to the squared radius, the area of the bulls-eye is squared (1/5) of the area of the target, i.e. (1/5)^2 = 1/25. This is the probability of the arrow landing on the bulls-eye. 1/25 can also be shown as 4/100, or 4% (4 percent).