Prior probabilities are often educated guesses at best, so it is worth performing a sensitivity analysis on their values. However, we must make sure that we vary them so that all probabilities are...

Prior probabilities are often educated guesses at best, so it is worth performing a sensitivity analysis on their values. However, we must make sure that we vary them so that all probabilities are nonnegative and sum to 1. For the Acme problem, perform the following sensitivity analyses on the three prior probabilities and comment on the results.

a. Vary the probability of great in a one-way sensitivity analysis from 0 to 0.6 in increments of 0.1. Do this in such a way that the probabilities of the two other outcomes, fair and awful, stay in the same ratio as they are currently, 7 to 4.

b. Vary the probabilities of great and fair independently in a two-way sensitivity analysis. You can choose the ranges over which these vary, but you must ensure that the three prior probabilities continue to be nonnegative and sum to 1. (For example, you couldn’t choose ranges where the probabilities of great and fair are 0.6 and 0.5.)