SOLUTION: 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

Question 1019452: 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, 72% of the valves meet the specification, 22% are reground, and 6% are scrapped. Furthermore, assume that of those valves that are reground, 45% meet the specification, and 55% are scrapped.
Find the probability that the valve meets the specification (after either the first or second grind).
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
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, 72% of the valves meet the specification, 22% are reground, and 6% are scrapped. Furthermore, assume that of those valves that are reground, 45% meet the specification, and 55% are scrapped.
Find the probability that the valve meets the specification (after either the first or second grind).

Solution:
A good example of using the probability tree:
After the first grind, there are three cases,
pass : 72%
regrind : 22%
reject : 6%

Of the 22% that requires a regrind,
pass : 45%
reject : 55%
Summary:
Parts that pass after the first grind = 72%
Parts that pass after he second grind = 22%*45% = 9.9%

Total parts that pass = 72+9.9%=81.9%
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