SOLUTION: A piece of wire 6 in long is cut into two pieces at a random point. What is the probability that both pieces of wire will be at least 1 in long?

Put the original piece of wire onto the number line, from 0 to 6.


Let x be the coordinate, where you cut.


Then the condition that both cuts will be at least 1 in long, is this inequality

1 < x < 5.


So,  the cutting position "x" must lie in the segment  [1,5]  of the entire piece of the length 6.


Hence, the probability under the question is   =  = 66.66%.