The factory has four initial component lots: 10, 20, 30, and 40. The mixing process involves randomly selecting two lots at each step to combine until only one lot remains. The factory's specific sequence of combinations is: first combining the 10-component lot with the 40-component lot, then combining the 20-component lot with the 30-component lot, and finally combining the two resulting 50-component lots.

1. Step 1: Combine two lots from the initial four.
   The number of ways to choose 2 lots out of 4 is given by the combination formula (C(4, 2)):
   [ C(4, 2) = \frac{4!}{2!(4-2)!} = 6 ]
   The possible pairs are: (10,20), (10,30), (10,40), (20,30), (20,40), (30,40).
   The factory's desired pair is (10,40), which is one of the six possible pairs. Thus, the probability for Step 1 is:
   [ \frac{1}{6} ]

2. Step 2: Combine two lots from the remaining three.
   After combining