The Quality Control Manager for the NKA Inc Based on Historical Data,if the Lot Is Poor Quality,40% of to Accept

The quality control manager for the NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)the shipment (lot)of incoming material.The historical data indicates that there is 30% chance that the lot is poor quality (S₁),50% chance that the lot is fair quality (S₂),and 20% chance that the lot is good quality (S₃).Assume the following payoff table is available.The values in the payoff table are in thousands of dollars. $$\begin{array} { l c c c } & { \text { States of Nature } } \\\text { Decision } & \mathrm { S } _ { 1 } & \mathrm {~S} _ { 2 } & \mathrm {~S} _ { 3 } \\\text { Accept } & 20 & 30 & 90 \\\text { Further analyze } & 60 & 70 & 15 \\\text { Reject } & 80 & 50 & 30\end{array}$$ Based on historical data,if the lot is poor quality,40% of the items are defective.If the lot is fair quality,22% of the items are defective.If the lot is good quality,10 % of the items are defective.The quality control manager inspects one unit from a recent shipment.
-After inspecting it,the manager determines that the unit is not defective.Based on this additional information,determine the revised (posterior)probabilities for each of the three states of nature.