A company is considering producing some new Gameboy electronic games. Based on p

Question

A company is considering producing some new Gameboy electronic games. Based on past records, management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure. Market research may be used to revise these probabilities. In the past, the successful products were predicted to be successful based on market research 90 percent of the time. However, for products that failed, the market research predicted these would be successes 20 percent of the time. Use the following to denote the events: S=Successful, F=Failure (Unsuccessful), PS=Predicted Success, PF=Predicted Failure. If market research is performed for a new product, what is the probability that the results indicate a successful market for the product and the product is actually not successful?

Explanation / Answer

Let,

MS be the event that management predicted Success

MF be the event that management predicted Failure

S be the event that the product was a success

F be the event that the product was a failure

P(MS) = 70%

P(MF) = 30%

P(MS | S) = 90%

P(MS | F) = 20%

Let P(S) = x

then P(F) = 1-x

P(MS) = P(MS | S) * P(S) + P(MS | F) *P(F)

or, 70% = 90%*x + 20% *(1-x)

or, x = 5/7

P(S) = 5/7

and P(F) = 2/7

P(MS and S) = P(MS | S) *P(S) = 90%*(5/7) = 64.2857%

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