A Manufacturing Company Introduces Two Product Alternatives

A Manufacturing company introduces two product alternatives. The table below provides profit payoffs in thousands of dollars.

The probabilities for the state of nature are P(Up) = 0.35, P(Stable) = 0.35, and P(Down) = 0.30.
A test market study of the potential demand for the product is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows:
P(F|Up) = 0.5; P(F|Stable) = 0.3; P(F|Down) = 0.2
P(U|Up) = 0.2; P(U|Stable) = 0.3; P(U|Down) = 0.5
Use Bayes' theorem to compute the conditional probability of the demand being up, stable, or down, given each market research outcome.