Question

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?

Answer 1

Answer:

The probability that the market will be actaully favourable is 0.9084

Step-by-step explanation:

Lets put names to the events

F = The market is favourable

U = The market is favourable (this is F^c)

PF = Gazelle predicts that the market is favourable

PU = Gazelle predicts that the market is unfavourable (this is PF^c)

Also, we know that

P(F) = 0.7

P(U) = 0.3

P(PF | F) = 0.85

P(PU | F) = 0.15

P(PF | U) = 0.2

P(PU | U) = 0.8

We want to know P(F |PF), we can obtain this probability using the ones that we are given and the Bayes Formula

$P(F | PF) = \frac{P(PF | F) \, * \, P(F)}{P(PF | F) * P(F) + P(PF | U) * P(U)} = \frac{0.85*0.7}{0.85*0.7+0.2*0.3} = 0.9084$

The probability that the market will be actaully favourable is 0.9084