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.If market research is performed for a new product, what is the probability that the product will be successful if the market research indicates a success?
A)0.10
B)0.90
C)0.91
D)0.63

Question

Quizplus · Accepted Answer

Using Bayes' theorem, we can calculate the updated probability:
P(success | market research indicates success) = P(market research indicates success | success) x P(success) / P(market research indicates success)
P(market research indicates success | success) = 0.9 (given)
P(success) = 0.7 (given)
P(market research indicates success) = P(market research indicates success | success) x P(success) + P(market research indicates success | failure) x P(failure)
P(market research indicates success | failure) = 0.2 (given), P(failure) = 0.3 (given)
P(market research indicates success) = 0.9 x 0.7 + 0.2 x 0.3 = 0.67
Putting all the values into the formula:
P(success | market research indicates success) = 0.9 x 0.7 / 0.67 = 0.91
Therefore, the probability that the product will be successful if the market research indicates a success is 0.91.

A Company Is Considering Producing Some New Gameboy Electronic Games