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Gazelle Consulting Group, has been engaged to perform a feasibility study to determine if the market for a proposed innovation will be favorable or not. Gazelle Consulting has done similar studies in the past and whenever the market was actually favorable, their market research study indicated that it would be favorable 85% of the time. On the other hand, whenever the market performance was unfavorable, Gazelle Consulting incorrectly predicted that the market would be favorable 20% of the time. Before Gazelle Consulting Group conducts the study, it is believed there is a 70% chance the market will be favorable. When Gazelle Consulting performs the study for this new product, the results predict the market will be favorable. What is the probability that the market will actually be favorable? Hint: Organize your information first, before solving the problem.

Respuesta :

Answer:

Given that the forecast is a favorable market. there is a 91% of chances the market will actually be favorable.

Step-by-step explanation:

This problem can be solved applying the Bayes theorem.

List of events:

F: market favorable

FF: forecast a favorable market

NF: market not favorable

FNF: forecast a not-favorable market

The information we have is:

P(FF | F) = 0.85

P(FF | NF) = 0.20

P(F) = 0.70

Now we need to calculate the chances of having a favorable market given that the forecast gives a favorable market P(

[tex]P(F|FF)=\frac{P(FF | F)*P(F)}{P(FF | F)*P(F)+P(FF|NF)*P(NF)}\\\\P(F|FF)=\frac{0.85*0.70}{0.85*0.70+0.20*0.30}=\frac{0.595}{0.595+0.060}=\frac{0.595}{0.655}= 0.91[/tex]

Given that the forecast is a favorable market. there is a 91% of chances the market will actually be favorable.

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