Subject: parachute Problem
A parachutist jumps from an airplane and lands in a square field that is 2 kilometers on each side. In each corner of the field there is a large tree. The parachutist's ropes will get tangled in the tree if she lands within 1/11 kilometer of its trunk. What is the probability that she will land in the field without getting caught in a tree?
In order to find the probability, we must, make two assumptions. first we must assume that the parachutist lands somewhere within the field; she does not land outside it. second, we assume that her landing point is random.
Under these assumptions, the probability of not getting caught in the tree is a ratio of areas. the sample space is the square field its area is 4 sq km. The event space is the shaded area its area is 4-(pi/121). The probability of landing in the shaded area is (4-(pi/121))/4, or approximately 0.99.
1. Rework the parachute problem, using a radius of 1/9 instead of 1/11. Now try a radius of 1/5.
In the equation it gives you I don't understand why you use pi and where they got the 121 from. I was thinking that maybe the four corners equal a circle and you could find the area of the circle cause you solve by going Area of trees divided by the area of the field, so the area of a circle is pi times r cubed but that equals some really weird number.
You are correct in your statement that "the four corners equal a circle" but the area of a circle is pi times r squared not r cubed. So the area of the "circle" that contains the tree is (writing * for multiplication) pi*r2 = pi*(1/11)2 = pi*(1/121) = pi/121.