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...

To find the probability that Bob scores 100 points from his first shot, we need to determine the favorable outcome (scoring 100 points) and the total number of possible outcomes.

Let's calculate the favorable outcome first. In order for Bob to score 100 points, the bullet must pass through the net without touching any wires. Given that the bullet has a diameter of 2 mm, it can pass through the net without touching the wires if it hits the center of any of the 5 mm square openings.

The center of each square opening is a point that is not occupied by the wires. Since the wires are 1 mm thick and the openings are 5 mm square, we can calculate the number of favorable outcomes by considering the number of centers of the square openings.

There are 5 openings horizontally and 5 openings vertically, resulting in a total of 5 x 5 = 25 square openings. Each square opening has a single center point, so there are 25 favorable outcomes.

Now, let's calculate the total number of possible outcomes. The bullet can hit any point within the area contained by the net. Since the net has a 5 mm spacing between the wires, we can consider the net as a grid of 5 mm x 5 mm squares.

There are 5 squares horizontally and 5 squares vertically, resulting in a total of 5 x 5 = 25 squares. Each square can represent a possible location for the bullet to hit without regard to where it centers in the opening, as long as it doesn't touch the wires.

Therefore, the total number of possible outcomes is 25.

Now we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

P(Scoring 100 points) = favorable outcomes / total outcomes = 25 / 25 = 1

So, the probability that Bob scores 100 points from his first shot is 1 or 100%.