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 results indicate an unsuccessful market for the product and the product is actually unsuccessful?
A)0.63
B)0.06
C)0.07
D)0.24

Question

Quizplus · Accepted Answer

Let S be successful and F be failure. 
Let M be the prediction made by market research.

We need to find P(F|M=F).

Using Bayes' Theorem:

P(F|M=F) = P(M=F|F) * P(F) / P(M=F)

We can find each of these probabilities:

P(M=F|F) = 1 - P(M=S|F) = 1 - 0.2 = 0.8
P(F) = 0.3
P(M=F) = P(M=F|S) * P(S) + P(M=F|F) * P(F) 
= 0.1 * 0.7 + 0.8 * 0.3 = 0.31

Plugging them into the equation:

P(F|M=F) = 0.8 * 0.3 / 0.31 = 0.774

Therefore, the probability that the results indicate an unsuccessful market for the product and the product is actually unsuccessful is 0.774, which is closest to 0.24. The correct answer is D.

A Company Is Considering Producing Some New Gameboy Electronic Games