Baxter Inc. is a medium-sized maker of lawn furniture. Their business is doing well and they are considering building a new manufacturing plant to handle potentially increased sales next year. Will next year's demand for lawn furniture be up (U) or down (D)? Baxter's own financial staff estimates a 60 percent chance that demand for lawn furniture will be up next year (P(U) = 0.6). These are their prior probabilities.
But Baxter's financial staff is not experienced in macroeconomic forecasting. Baxter is considering whether to engage an expert market analyst who has wide experience in forecasting demand for consumer goods. In terms of predicting directional (+ or ?) changes in demand, she has been correct 80 percent of the time. If the expert is hired, Baxter could revise its estimate, using two conditional probabilities: P(Expert says “up”|U) = 0.8   P(Expert says “down”|D) = 0.8
What Baxter really wants to know is the chance the demand will go up if the expert says the demand will go up (P(U|Expert says “up”). Compute this probability for Baxter.