A company is considering producing a new Gameboy electronic

A company is considering producing a new Gameboy electronic game. Based on past records, management believes there is a 70% chance that the market for the new game will be good and a 30% chance that the market for the new game will be poor. However, management would like to use market research to revise these probabilities. In the past, whenever the market for a new game actually was good, market research correctly indicated the market would be good 85% of the time. However, whenever the market for a new game was actually poor, the market research incorrectly indicated that the market would be good 20% of the time. The current market research is predicting that the market for the new game will be good. Given the market research prediction, what is the probability the market will actually be good?
0.631
0.908
0.079
0.247
0.572

Solution

Based on past records, management believes that there is a 70 percent chance that each of these will be successful.

In the past, the successful products were predicted to be successful based on market research 90 percent of the time

Therefore,

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

P(Predicted successful and Actual Failure) = .20 x .30 = .06.