Question

A company is considering producing some new products. Based on past records, management believes that there is a 70% chance that each of these will be successful, and a 30% chance of products were predicted to be successful based on market research 90% of the time. However, failure. Market research may be used to revise these probabilities. In the past, the successful for products that failed, the market research predicted these would be successes 20% of the time.

Answer 1

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

What is probability?

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Events:

S: success

F: failure

MS: market research forecast a success

MF: market research 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 per cent 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:

$P(MF|F) = \dfrac{P(F|MF)\times P(F)}{P(F|MF)\times P(F)+P(S|MF)\times P(S)}$

$P(MF|F) =\frac{(0.8\times 0.3)}{0.8\times 0.3)+(0.1\times 0.7}$

$P(MF|F) =\dfrac{0.24}{0.31}=0.77$

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

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