A circular dartboard has radius 20 cm and a central bull of radius 5 cm. A dart thrown at the board is equally likely to land at any point of it. What is the probability that the dart lands inside the bull?

For a point chosen at random the probability is a ratio of AREAS, not of radii. Area of the bull = π$(5{)}^2=25$π and area of the whole board = π$(20{)}^2=400$π, so the probability is 25π/400π = 1/16. Comparing the radii 5 : 20 gives 1/4 and forgets that area grows as the square of the radius — a quarter of the radius means a sixteenth of the area.