BTGmoderatorAT wrote:A 5 meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point?

A) 1/6
B) 1/5
C) 3/10
D) 1/3
E) 2/5

I'm confused how to set up the formulas here. Can any experts help?

We see that in order for the area of the square to be more than 1 square meter, the side of the square has to be more than 1 meter. That is, the perimeter of the square has to be more than 4 meters.

If the wire is cut no more than 1 meter from one end of the wire, then obviously the longer piece of the wire will have a length of at least 4 meters. That is, the area of the square will be at least 1 square meter. Therefore, the probability that the wire will have a longer piece that is at least 4 meters when it's cut from one end of the wire is 1/5 (since it can be cut at any point that is no more than 1 meter from that end of the wire). However, since the wire has two ends, we can cut the wire no more than 1 meter from each of its two ends; therefore, the probability that the wire will have a longer piece that is at least 4 meters when it's cut from either end is 1/5 x 2 = 2/5.

Answer: E