Question: A research group is contemplating purchase of a new software package to perform some specialized calculations. The systems manager decides to do two sets of diagnostic tests for significant bugs that might hamper operation in the intended application. The tests are carried out in an operationally independent manner. The following analysis of the results is made.

· H = the event the program is satisfactory for the intended application

· S = the event the program is free of significant bugs

· E1 = the event the first diagnostic tests are satisfactory

· E2 = the event the second diagnostic tests are satisfactory

Since the tests are for the presence of bugs, and are operationally independent, it seems reasonable to assume {H, E₁, E₂}ci|S and {H, E₁, E₂}ci|S^c Because of the reliability of the software company, the manager thinks P (S) = 0:85. Also, experience suggests

P(H|S) = 0.95      P(E₁|S) = 0.90      P(E₂|S) = 0.95

P(H|S^c) = 0.30      P(E₁|S^c) = 0.20      P(E₂|S^c) = 0.25

Determine the posterior odds favoring H if results of both diagnostic tests are satisfactory.