#No 3 please me solved no3 thanks Consider an automobile manufacturer who is con

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#No 3 please me solved no3 thanks

Consider an automobile manufacturer who is contemplating the redesign of an existing model. The engineering and marketing groups have concurrently determined that there are three feasible redesign alternatives from which to choose. Due to an uncertain future budget, the following information is available: Design 1 will be chosen with probability 0.3 Design 2 will be chosen with probability 0.5 Design 3 will be chosen with probability 0.2 The marketing department has determined (through extensive forecasting studies) that: If design 1 is chosen, total revenues will increase with probability 0.8 If design 2 is chosen, total revenues will increase with probability 0.1 If design 3 is chosen, total revenues will increase with probability 0.4 Compute the probability that a redesign will increase revenues. Using the data given in problem 2, now suppose that a redesign was implemented and that revenues did, in fact, increase. What is the probability that the manufacturer chose to implement design 2?

Explanation / Answer

P(design 1) = 0.3

P(design 2) = 0.5

P(design 3) = 0.2

P(revenue increases | design 1) = 0.8

P(revenue increases | design 2) = 0.1

P(revenue increases | design 3) = 0.4

P(revenue increases) = P(revenue increases | design 1) * P(design 1) + P(revenue increases | design 2) * P(design 2) + P(revenue increases | design 3) * P(design 3)

                                   = 0.8 * 0.3 + 0.1 * 0.5 + 0.4 * 0.2

                                   = 0.37

P(design 2 | revenue increases) = P(revenue increases | design 2) * P(design 2) / P(revenue increases)

                                                    = 0.1 * 0.5 / 0.37

                                                    = 0.1351

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