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

87%

Explanation:

The computation of the likelihood for high demand is as follows:

Given that

The high consumer demand probability = P(H) = 0.6

The low consumer demand probablity = P(L) = 0.2

The Probability of favorable survey response given high consumer demand = P(F ÷ H) = 0.9

And,

Probability of favorable survey response given low consumer demand = P(F ÷ L) = 0.2

Now, determine the probability of high demand that the market report is favorable = P(H ÷ F)

P(H ÷ F) = (P(F ÷ H) × P(H)) ÷ (P(F ÷ H) × P(H)) + (P(F ÷ L) × P(L))

= ((0.9) × (0.6)) ÷ ((0.9 × 0.6) + (0.2 ×  0.4))

= 0.87096

= 0.87096 × 100

= 87%

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