Question: An aircraft company is considering using a new light-weight fastener, called the Superlight, to rivet certain sheet metal parts together. These particular items are not critical to safety, and so the decision is purely financial. Using Super lights instead of the basic fastener would save a value of $100 K to the aircraft manufacturer.
The Superlight fastener has never been used before on a production aircraft, and engineers are wary of its durability. From what little they know of the design and initial lab tests, they have high uncertainty about the number of Superlight fasteners that would need replacement during routine maintenance. They translate this to costs of $300 K with probability of 0.3, $120 K with probability 0.5, and $75 K with probability 0.2. (Label these possible cases High, Moderate, and Low repair cost, for future reference.) These costs include both parts and labor
The alternative to the Superlight is the Basic fastener, which, although heavier than the Superlight, has been used extensively on past aircraft. Stress engineers feel that the Basic has a "tried and true" performance record: They conclude from past statistics that the repair cost associated with Basic fastener failure is $125 K. In these dollar ranges, assume that the aircraft company is a risk-neutral decision maker.
What probability of high repair costs leads to the highest value of clairvoyance on repair costs? Again, when you vary the probability, keep the ratio of the other two probabilities constant.