Question below because it is to long

Question

A soldier is parachute training. He jumps out of a plane high enough that the pilot determines the soldier will land somewhere in the 240ft. radius landing zone. The pilot forgot to mention to the soldier that the parachute has very little maneuverability and there are 10 trees in the landing zone. Each tree from the air practically outlines a circle with a radius of 8ft. What is the probability that the soldier will land in a tree?

Please explain how to get the answer and the steps.

Answer 1

Hello Alia. This is an area question. If you know the entire area, and you also know the area covered by trees, you can discover the probability that the parachuter will land on an area covered by trees.

Recall that the area of a circle is pi(r^2)

Larger area: pi(240^2) = 57,600pi

Area covered by each tree: pi(8^2) = 64pi

There are ten trees: 64pi * 10 = 640pi

Probability can be thought of as the number of ways you get what you want divided by all possibilities. So, if I were betting at Vegas that the parachuter would land on a tree, I win if it lands anywhere in that 640pi area out of (meaning divided by) 57,600pi. That is a mere .011 or 1.1%.

I hope this helps!

David

Answer 2

The area of a circle is π*r². So the area if the landing zone is 240*240π square feet.

The area of 10 circles (tree areas) is 10*8*8π square feet.

Total tree area / landing zone area is 640/57,600 and that simplifies to 1/90 or about 0.0111 (rounded), and that is the probability. Or approximately 1.11%.