Question

Hannah's office department started a new birthday tradition. The birthday person is spun around and then throws a dart at the birthday poster, pictured below, to determine their prize.

24 inches
24 inches

If the dart lands in the triangle, the coworkers buy the birthday person lunch. If the dart lands in the circle, the coworkers buy the birthday person a cake. If the dart lands on the poster, but not in the circle or triangle, the coworkers just sing the Happy Birthday song.

If it is equally likely for Hannah to throw the dart anywhere on the poster, what is the probability that Hannah will get a cake? (Note: The diameter of the circle and the base and height of the triangle measure 12 inches.)

Answer choices:
A. π/8
B. 1/16
C. π/16
D. 1/8

Answer 1

1) Area of the poster:side * side = 24in * 24 in = 576 in^2

2) area of the circle: π * (radius)^2 = π (12 in / 2)^2 = 36π in^2

3) probability of landing in the circle = area of the circle / area of the poster

=> 36π / 576 = π / 16.

Answer: option C. π / 16