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
OA:
That the area of the square is more than 1 square meter means that the perimeter of the square is more than 4 meter. Imagine the wire is divided into 5 pieces:
0__1__2__3__4__5
I see that if we cut the wire at any point from 0 to 1 or any point from 4 to 5, we will have a long wire whose perimeter is more than 4 meter.
If we cut the wire at any point from 1 to 4, we get a long wire whose perimeter is less than 4 meter.
Undoubtedly, we have 3 choices if we cut the wire: from 0 to 1, from 1 to 4, and from 4 to 5. Following this reasoning, I think the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point should be 2/3.
Please explain what is wrong with my explanation?![]()
A. 1/6
B. 1/5
C. 3/10
D. 1/3
E. 2/5
OA:
[Reveal] Spoiler:
E
That the area of the square is more than 1 square meter means that the perimeter of the square is more than 4 meter. Imagine the wire is divided into 5 pieces:
0__1__2__3__4__5
I see that if we cut the wire at any point from 0 to 1 or any point from 4 to 5, we will have a long wire whose perimeter is more than 4 meter.
If we cut the wire at any point from 1 to 4, we get a long wire whose perimeter is less than 4 meter.
Undoubtedly, we have 3 choices if we cut the wire: from 0 to 1, from 1 to 4, and from 4 to 5. Following this reasoning, I think the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point should be 2/3.
Please explain what is wrong with my explanation?