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Misty Inc. launches a new range of perfumes for men and women. The probability of high consumer demand for the product is 0.6 and low consumer demand is 0.4. The probability of a favorable survey response given high consumer demand is 0.9 and the probability of a favorable survey response given low consumer demand is 0.2.
-If the marketing report is u'favorable, what is the probability of low demand?
A) 84%
B) 90%
C) 87%
D) 80%

Question

Quizplus · Accepted Answer

The probability of low demand given a favorable survey response can be calculated using Bayes' theorem. Let $ P(L) $ be the probability of low demand (0.4), $ P(H) $ the probability of high demand (0.6), $ P(F|L) $ the probability of a favorable response given low demand (0.2), and $ P(F|H) $ the probability of a favorable response given high demand (0.9). We want to find $ P(L|F) $, the probability of low demand given a favorable response.$$ P(L|F) = \frac{P(F|L)P(L)}{P(F|L)P(L) + P(F|H)P(H)} $$$$ P(L|F) = \frac{0.2 \times 0.4}{(0.2 \times 0.4) + (0.9 \times 0.6)} $$$$ P(L|F) = \frac{0.08}{0.08 + 0.54} $$$$ P(L|F) = \frac{0.08}{0.62} $$$$ P(L|F) \approx 0.129 $$ or 12.9%, which is not among the options provided. However, it seems there might have been a misunderstanding in the calculation or the interpretation of the options. Given the options, recalculating or reinterpreting the provided options might be necessary. The correct approach involves using Bayes' theorem as shown, but the final calculation should align with the options given. It appears there was a mistake in the calculation or in the interpretation of the question's intent. The correct calculation should reflect the probability of a specific outcome based on the given probabilities and the use of Bayes' theorem.

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