A line segment of length 5 is broken at two random points along its length. What is the probability that the shortest of the three new segments has length longer than 1?
+118608 I would use probablility contour mapping to answer this question.
A line segment of length 5 is broken at two random points along its length. What is the probability that the shortest of the three new segments has length longer than 1?
Let the lengths be x, 5-y and y-x
Note that when you add all these you get a lenght of 5 
so
0
Lets graph that.
The darkest area represents the entire sample space. How much area does it have?
Area = 0.5*5*5 = 12.5 units squared
Now how much of this sample space will have the shortest side bigger than than 1 unit?
mm
I think it is a lot easier to graph the sample space where one side is less than 1.
These are mutually exclusive and exhaustive events so their probabilities will be add up to 1
The lengths are x, 5-y and y-x
When will a length be LESS than 1 unit
\(0
The dark shaded area is where there IS a side that is less then one unit.
SO the triangle in the middle is where there is NO SIDE less than 1 unit.
Area of trianlge in middle = 0.5*2*2 = 2 units squared.
So the probability that the shortest length will be longer than 1 unit is \(\frac{2}{12.5}= \frac{4}{25}=\frac{16}{100}=16\%\)
