A stick is broken at two points. If the length of the stick is 6, then what is the probability that all three resulting pieces are shorter than 3 units?
Let the 3 pieces by x, 6 - y and y-x long
Note that when you add these up you get 6
You know that each of these must be between 0 and 6 units long.
GRAPH the sample space. Find Area of sample space
Now overlay that with the desired area where all the pieces are less than 3 units long. Find the area of this event
Probability = area of event/ area of sample space
This is called probability contour mapping.