Refer to the previous question. A manufacturing engineer for MPI collected the following data on the failure rates of components X, Y, and Z in a random sample of 1,000 circuit boards:

For example, the first row in this table indicates that components X, Y, and Z all passed their inspections in 710 out of the 1,000 boards checked. The second row indicates that 45 boards passed inspection on components X and Z, but failed on component Y. The remaining rows can be interpreted similarly.
a. Using this data, compute conditional probabilities for the decision tree you developed in question 13. (P(A|B) =P(A∩ B)/P(B) and P(A|B ∩ C) = P(A∩ B ∩ C)/ P(B ∩ C).)
b. According to the revised probabilities, in which order should the components be tested?
c. What is the expected cost of performing the tests in thissequence?

Transcribed Image Text:

X YZNumber of Boards 710 45 110 10 95 10 10 10 1000 Total: (p pass, f fail)