In the process of producing engine valves, the valves are subjected to a first grind. Valves whose thicknesses are within the specification are ready for installation. Those valves whose thicknesses are above the specification are reground, while those whose thicknesses are below the specification are scrapped. Assume that after the first grind, 70% of the valves meet the specification, 15% are reground, and 15% are scrapped. Furthermore, assume that of those valves that are reground, 90% meet the specification, and 10% are scrapped.

Find the probability that a valve is scrapped. Round the answer to three decimal places?

Given that a valve is scrapped, what is the probability that it was ground twice?