The probability of termination of the project before the engineering work has started, is:

Suppose a project manager is involved in a commercial speculative building development. For economic viability, the cost estimate for the structure, after engineering and design are complete, cannot exceed $Budget. The project manager can retain a structural engineer to design the building in steel or in concrete, or both, and to make the necessary engineer’s cost estimates, $Steel and $Concrete, when the designs are complete. If one or both of the designs is less than the budget, the project manager will choose the smaller and the project will proceed; otherwise it will be terminated. Therefore, using the identity between joint probability distributions and conditional probability distributions, the probability of termination of the project before the engineering work has started, is: