A snack food producer is considering introducing a new product to the consumer m

Question

A snack food producer is considering introducing a new product to the consumer market. It can choose to build a new facility for production of the new product, use an existing facility, or outsource the production to another company. The company estimates that the probability of strong demand for this product to be 65% and the probability of weak demand is estimated at 35%. The company also has the option to hire a marketing research firm to conduct a study to provide additional information about the demand. Historically, this research firm has predicted a strong demand when the eventual demand was strong 80% of the time, and has predicted a weak demand when the eventual demand was weak 85% of the time. What is the probability that the market research study will predict a strong demand?

Explanation / Answer

The eventual demand probability are given as,

P(eventual demand is strong) = 0.65

P(eventual demand is weak) = 0.35

Also the conditional probability given in the problem are,

P(study predicts strong demand | eventual demand is strong ) = 0.80

P(study predicts weak demand | eventual demand is weak) = 0.85

The required probability would be given by,

P(market research study will predict a strong demand) = P(eventual demand is strong)*P(study predicts strong demand | eventual demand is strong) + P(eventual demand is weak)*P(study predicts strong demand | eventual demand is weak)

or,

P(market research study will predict a strong demand) = 0.65*0.80 + 0.35*(1-0.85) = 0.5725

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