In an advertisement campaign a marketing firm conducted a su

In an advertisement campaign, a marketing firm conducted a survey to determine the effectiveness of the campaign for a given product. The results show that 20% of customers purchased the product, 44% recalls seeing the advertisement, and 12% of the customer who purchased the product and recalled seeing the advertisement.

a. What is the probability of an individual purchasing the product given that given the customer recall seeing a product?

b. If the advertising cost is minimal and the objective is increasing the market share, should the advertisement be continued or not (if yes why if not why not?)

Solution

a)

P(purchase|see) = P(purchase and see) / P(see)

As

P(purchase and see) = P(purchase) P(see|purchase) = 0.20*0.12 = 0.024

Thus,

P(purchase|see) = P(purchase and see) / P(see) = 0.024/0.44 = 0.054545455 [answer]

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b)

As P(purchase|see) < P(purchase), then they should not continue. Those who see the advertisement, it turns out, are even less likely to purchase that the whole population.