A certain transistor is manufactured at three factories located at places X, Y, and Z. It is known that the X factory produces twice as many transistors as the Y factory, which produces the same number as the Z factory during the same period. Experience also shows that 2% of the transistors produces at X and Y are faulty and so are 4% of those produced at Z. A service engineer, while maintaining electronic equipment, finds a defective transistor. What is the probability that the factory Y is to blame?