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, 73% of the valves meet the specification, 21% are reground, and 6% are scrapped. Furthermore, assume that of those valves that are reground, 46% meet the specification, and 54% are scrapped. Given that a valve meets the specification, what is the probability that it was ground only once?

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
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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, 73% of the valves meet the specification, 21% are reground, and 6% are scrapped. Furthermore, assume that of those valves that are reground, 46% meet the specification, and 54% are scrapped. Given that a valve meets the specification, what is the probability that it was ground only once?
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