I can only try-
That’s the answer the I got. Here’s how I did it:
For the two machines, let’s call them x and y, plot their lives on a 15 * 15 graph with the life of x on the x-axis and the life of y on the y-axis. Draw a 45 degree angle line from the origin to 15,15 to show the possible places where x can break down. (It’s a straight line since any point in time has an equal probability of the machine breaking down there.)
Now draw two more 45 degree angle lines, the first should be shifted one unit to the left of the first line and the other one should be shifted one unit to the right of the first one. The area created by those two lines and bounded by the 15 * 15 graph is 1-196/225 = 12.88889%.
The way I calculated the area is by first calculating the “negative” area and subtracting. On the outside there are two triangles with the same area. Each is a right triangle with legs of length 14. the area is (14 * 14)/2, therefore the are of both triangles is 14 * 14 = 196. The total area of the graph is 15 * 15 = 225. Subtracting the triangles from the graph gives us 1 – (196/225) = 12.888889%.
Do you want to publish a paper on this with me? You can earn an Erd?s number of 5.