# Question on a Decision Tree Probability (Scenario 3)

#### webster111

##### New member
I have a question on the probabilities / formula(s) to use for the Third Scenario in a Decision Tree question: I'm OK with Scenario 1 and 2, but am scratching my head with Scenario 3 - we did not do Bayes' theorem and I'm not sure if I could go ahead working out probabilities based on the last section and only calculate the EMVs with the provided probability info at the end:

Scenario 3: Introduce a new range with prior market research costing $50000. The market research will indicate whether future sales are likely to be good or bad. If the research report indicates future sales as good, then the management will spend an extra$40000 on capital equipment, which would increase the annual profit by $30000 provided sales are actually high. However, if sales are actually low, then the annual profit would drop by$10000. However, should management decide not to spend more on promotion (given a good research report), then profit levels would be as for scenario 2.

If the research report indicates future sales as bad, then management will scale down their expectations to an annual profit of $45000 if sales are actually low. However, if actual sales do turn out to be high, profits can only rise to$75000 because of capacity constraints.

This is my confusion part of the question:
Probability calculations, based on historical performance of the company, reveal the following information:
Probability of a favorable research report = 0.60.
Probability of high sales given a favorable research report = 0.90.
Probability of high sales given an unfavorable research report = 0.35.

This - Probability of a favorable research report = 0.60. - tells me I don't need to do Bays. Or am I incorrect?

Thank you

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