Question: (20 points total) The Alpha Company is trying to decide whether to market a new product. As in many new-product marketing situations, there is considerable uncertainty about whether the new product will eventually “catch on.” Alpha believes that it might be wise to introduce the product in a regional test market before introducing it nationally. Therefore, the company’s first decision is whether to conduct the test market. If Alpha decides to conduct the test market, it must then wait for the results of the test market. Based on these results, it can then decide whether to market the product nationally or abandon the new product altogether. On the other hand, if the original decision is not to conduct a test market, then the decision – whether to market the product nationally or abandon the new product – can be made immediately. Furthermore, Alpha has estimated that without a regional test, the new product is equally likely to be successful or to fail nationally. Alpha has also estimated that if the new product is a “good” product (i.e., it will be successful nationally), then the probability that the regional test is positive is 0.84 (which implies that the probability of a negative regional test is 0.16); if the new product is a “bad” product (i.e., it will fail nationally), then the probability that the regional test is negative is 0.64 (which implies that the probability of a positive regional test is 0.36).

“To test market or not to test market?”

(a) Compute the probability table for this problem. (Use S and F to denote the event of a national success and failure, respectively; use P and N to denote the event of a regional positive result and negative result, respectively.)

(b) What is the conditional probability of a national success given that the test market result is positive? What is the conditional probability of a national failure given that the test market result is negative?