The probability of success = V(success)/V(all possibilities) = (1/2)/1 = 1/2 Thus the volume of the success region = 1 – 3(1/6) = 1/2 The same is true of the failure region for b and c. The volume of the failure region for a = 1/6. The volume of the entire solution space = 1, the volume of a cube of side 1. Thus the volume of the failure region is 1/3Bh = 1/3(1/2)1 = 1/6. The failure volume is a 3-sided pyramid with height = 1 and base = 1/2. The failure area is a triangular region that runs from (0, 0) to (a,0) and then to (0, a). The line intercepts the b-axis at a and the c-axis at a. This line separates the two regions of success and failure. For any given a we can draw a plot of the line a = b+c. When a > b+c, the ends cannot touch to form a triangle.įor simplicity we used the interval. When a = b+c it means that the opposite sides just touch and the 3 line segments overlap to form a single line segment. If they are not, then a triangle is not formed. That means that the two opposite sides together must be longer. If a is the longest side it means that b+c > a.
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