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. 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

Answer 1

Answer:

The probability that the results indicate an unsuccessful market for the product and the product is actually unsuccessful is P=0.77.

Step-by-step explanation:

Events:

S: success

F: failure

MS: market research forecast a success

MF: market reasearch forecast a failure

The information we have is:

P(S)=0.70

P(F)=0.30

P(S|MS)=0.90

P(F|MS)=0.20

If P(F|MS)=0.20, we can derive that P(F|MF)=0.80. That is, the failed products were predicted to be a failure based on market research 80 percent of the time.

We also can conclude that P(S|MF)=0.10.

We can calculate the probability of having a forecast of a failure, given that the product is actually unsuccessful as:

$P(MF|F)=\frac{P(F|MF)*P(F)}{P(F|MF)*P(F)+P(S|MF)*P(S)} =\frac{0.8*0.3}{0.8*0.3+0.1*0.7}=\frac{0.24}{0.24+0.07}\\\\P(MF|F)=\frac{0.24}{0.31}= 0.77$

The probability that the results indicate an unsuccessful market for the product and the product is actually unsuccessful is P=0.77.