OUESTION $5$: Decision Analysis $-$ Posterior$/$Revised Probability

The NBS television network has to decide whether to air a show or not air a show. If the show is aired

then the NBS television network earns an average of $$700,000$ from a hit show and loses an average of

$$150,000$ on a flop. Of all shows reviewed by the network, $20\%$ turn out to be hits and $80\%$ turn out to be

flops. For $$50,000,$ a market research firm will have an audience view a pilot of a prospective show and

give its view about whether the show will be a hit or a flop. If a show is actually going to be a hit, there is

a $90\%$ chance that the market research firm will predict the show to be a hit. If the show is actually going

to be a flop, there is an $85\%$ chance that the market research firm will predict the show to be a flop.

a$)$ Calculate all the posteriors$/$revised probabilities.

b$)$ Determine how the network can maximize its expected profits $($i$.$e$.,$ maximize its EP$).$ Make sure to

provide a managerial statement for the decision strategy $($i$.$e$.,$ Verbally communicate the decision strategy$).$

Find the Expected Value of Sample information $($EVSI$),$ which is the maximum amount that the network is

willing to pay the market research firm $($decision tree plotting will not be discussed in review session however

the solutions will be provided$)$