A market research firms conducts studies regarding the success of new products. The company is not always perfect in predicting

Question

3 months ago

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A market research firms conducts studies regarding the success of new products. The company is not always perfect in predicting

the success. Suppose that there is a 50% chance that any new product would be successful (and a 50% chance that it would fail). In the past, for all new products that ultimately were successful, 80% were predicted to be successful (and the other 20% were inaccurately predicted to be failures). Also, for all new products that were ultimately failures, 70% were predicted to be failures (and the other 30% were inaccurately predicted to be successes). For any randomly selected new product, what is the probability that the market research firm would predict that it would be a success?

Mathematics

1 answer:

AnnZ [12.3K] · Answer 1 · 2026-03-04T00:15:47+03:00

Response: The calculated probability is 0.7273.

Step-by-step breakdown:

According to the provided data:

Successes Failures Total

Forecasted successes 0.4 0.15 0.55

Forecasted failures 0.1 0.35 0.45

Total 0.5 0.50 1

This shows the likelihood of the market research agency predicting success.

P(Actual success|Predicted success) is calculated as:

$\dfrac{0.4}{0.55}=0.7273$

Therefore, the determined probability is 0.7273.