A machine is used in a production process up correctly machi

A machine is used in a production process. up correctly.) machine is set up correctly, it produces 100%-95%-5% unacceptable items.) 100%-40%-60% unacceptable items.) From past data, it is known that 97% of the time the machine is set up correctly. (This implies that 100%-97%-3% of the time he machine is Not set Furthermore, it is known that if the machine is set up correctly, it produces 95% acceptable (non-defective) items. (This implies that if the However, when it is set up incorrectly, it produces only 40% acceptable items. (It implies that if the machine is set up in correctly, it produces By using the notation A1 for the event of \"machine is set up correctly\" Az for the event of \'machine is not set up correctly G for the event of \"machine produces acceptable items\" B for the event of \'machine produces unacceptable items\" The above given information can be denoted as HA!) = 0.97 , HA) = 0.03 Given that the selected item is unacceptable, use the Bayes\' Theorem method to find the probability that the machine is set up correctly? It means that find the value of PAIB) . show your result with four digits on the right side of decimal point that find the value of PA1B. Show your result with four digits on the right side of decimal point. Hint: Use the format and the steps of Table 4.7 listed below, and use the given data, the first number in your fifth column is the solution.)

Solution

Here,

P(B) = P(A1) P(B|A1) + P(A2) P(B|A2) = 0.97*0.05 + 0.03*0.6 = 0.0665

Hence,

P(A1|B) = P(A1) P(B|A1)/P(B) = 0.97*0.05/0.0665 = 0.729323308 [ANSWER]