posted by bob on .
Bob and Jack play a shooting game. In this
game, they have a net at a distance. The net is
made up of 1 mm thick wires. The wires run
vertically and horizontally to form a mesh that
has 5 mm square openings between them. A
bullet 2 mm in diameter must be shot in such a
way that it goes through the net without
touching the wires. Such a shot would result in
100 points. All other scenarios will result in 0
points. Bob is set to start the game. What is
the probability that Bob scores 100 points
from his first shot?
area of 5mm square: 25mm^2
cross-section of 2mm bullet = 3.14mm^2
portion of square occupied by bullet: 3.14/25 = 0.126
So, there's a 1-.126 = .874 chance the bullet will not hit the wires.
Actually, the dimensions need to be adjusted slightly to account for the space occupied by the wires, since he's firing at the mesh, not a single opening. I'm sure you can handle that.
Are you just posting the NSF POM's online for the answer? I am disappointed...