M14-17

Official Solution:

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. \(\frac{1}{6}\)
B. \(\frac{1}{5}\)
C. \(\frac{3}{10}\)
D. \(\frac{1}{3}\)
E. \(\frac{2}{5}\)


In order the area of a square to be more than 1, its side must be more than 1, or the perimeter must be more than 4. Which means that the longer piece must be more than 4. Look at the diagram below:



If the wire will be cut anywhere at the bolded region, then the rest of the wire (longer piece) will be more than 4 meter long. The probability of that is \(\frac{2}{5}\) (2 red pieces out of 5).


Answer: E