Question 1

The XYZ Corporation has offers on two contracts A and B. Suppose the proposal team made the following subjective probability assessments: the chance of winning contract A is 40 percent, the chance of winning contract B is 20 percent, the chance of winning contract A or B is 60 percent, and the chance of winning both contracts is 10 percent.

Part A

Explain why the above set of probability assignments is inconsistent with the axioms of probability.

Part B

What must P(B) equal such that it and the set of other assigned probabilities specified above are consistent with the axioms of probabilities

Question 2

Show the Bayes' rule is the basis for the equations below

Part A

P(H|e1) = (P(H)P(e1|H) / (P(H)P(e1|H) +(1-P(H))P(e1{H^c)

Part B

P(H|e1e2) = P(H|e1)P(e2|H) / P(H|e1)P(e2|H) + (1d-P(H|e1))P(e2| H^c)

Part C

P(H|e1e2e3) = P(H|e1e2) P(e3|H) / P(H|e1e2) P(e3|H) +(1-P(H|e1e2)|e1))P(e3| H^c)