Use the information below to answer the following question(s)
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.
-What is the likelihood for high demand knowing that the market report is favorable?
A) 84%
B) 90%
C) 87%
D) 80%

Question

Quizplus · Accepted Answer

We need to find the likelihood for high demand (H) given a favorable market report (F). This can be represented using Bayes' theorem as:

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

We are given:
- P(H) = 0.6 (probability of high consumer demand)
- P(F|H) = 0.9 (probability of favorable survey response given high consumer demand)
- P(H') = 0.4 (probability of low consumer demand)
- P(F|H') = 0.2 (probability of favorable survey response given low consumer demand)

To find P(F), we use the law of total probability:
P(F) = P(F|H) * P(H) + P(F|H') * P(H')
P(F) = 0.9 * 0.6 + 0.2 * 0.4
P(F) = 0.6

Substituting the given values in Bayes' theorem:
P(H|F) = (0.9 * 0.6) / 0.6
P(H|F) = 0.9 or 90%

Therefore, the likelihood for high demand knowing that the market report is favorable is 90%. The correct answer is option C.

Use the Information Below to Answer the Following Question(s)