Question

AnnoyCo, a large consumer products firm, has recently introduced a new product. As part of the launch, 25% of the customers in the company’s data base received calls from AnnoyCo’s telemarketers. It is now one year after the launch. 40% of the customrs in the company’s database have purchased the product, A recent survey by the company’s marketing department has determined that among customers who bought the product, one out of eight were called.

Q: Did telemarketing help the company’s sales?

Answer 1

Let C and ~C be the event that the customers were called or not called respectively.

Let B and ~B be the event that the customers bought or not bought the product respectively.

P(C) = 0.25

P(~C) = 1 - 0.25 = 0.75

P(B) = 0.4

P(C | B) = 1/8 = 0.125

P(~C | B) = 1 - 0.125 = 0.875

P(B | C) = P(C | B) * P(B) / P(C)

= 0.125 * 0.4 / 0.25

= 0.2

P(B | ~C) = P(~C | B) * P(B) / P(~C)

= 0.875 * 0.4 / 0.75

= 0.47

Thus, only 20% of the customers bought the product who were called but 47% of the customers bought the product who were not called. Thus, telemarketing did not help much in the company’s sales.