A company is considering producing some new boy electronic games Based records.

Question

A company is considering producing some new boy electronic games Based records. Management believers that there is a 70 percent chance that each of these will be successful a 30 percent chance of failure Market research may be used to reverse these probabilities In the past, the unsuccessful products were predicted to be successful based on market research 90 percent of the However, for products that failed the market research predicted these would be succeeds 20 percent of the time If market research is performed for a new product. What is the probability then the results indicate a successful market for the product and the product actually as successful?

Explanation / Answer

let S be the event that the game is successful and F be the event that the game is failure.

and M be the event that the market research says that the game is successful.

in the past successful products were predicted to be successful by the market research 90% of the times

and failure products were predicted to be successful by the market research 20% of the times

a game has 70% chance of being successful and 30% chance of being failure.

so P[S]=0.7 P[F]=0.3   P[M|S]=0.9   and P[M|F]=0.2

hence the probability that the results indicate a successful market for the product and the product is actually successful is

P[S|M]=P[M|S]*P[S]/P[M]   [by Bayes' theorem]

          =P[M|S]*P[S]/{P[M|S]*P[S]+P[M|F]*P[F]}   [by complete porbability theorem]

          =(0.9*0.7)/(0.9*0.7+0.2*0.3)=0.63/0.69=0.913 [answer]

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