Question

In a survey, 2,400 cable company subscribers were asked to share their complaints about the cable service. The number one complaint was the time to get through to a customer representative, with 17% of the participating consumers selecting it. Several other complaints were noted, including impolite customer reps (14%), poor customer service (14%), payment disputes (11%), incorrect billing (10%), incompetent complaint handling (8%), and indifference to customers (7%). These complaint categories are mutually exclusive. Assume that the results of this survey can be extended to all cable subscribers. If a cable subscriber is randomly selected, determine the following probabilities. a. The subscriber complains about payment disputes or incorrect billing. b. The subscriber complains about indifference to customers and incompetent complaint handling. c. The subscriber complains about impolite customer reps given that the subscriber complains about incorrect billing. d. The subscriber does not complain about incompetent complaint handling nor does the consumer complain about payment disputes.

Answer 1

Let P =Probability

a.

P(The subscriber complains about payment disputes or incorrect billing) =11% + 10% =21% =0.21

b.

P(The subscriber complains about indifference to customers and incompetent complaint handling) =0

(since they are mutually exclusive events, they cannot happen simultaneously. So, their joint probability =0).

c.

P(The subscriber complains about impolite customer reps given that the subscriber complains about incorrect billing) =0

(since the conditional probability of two mutually exclusive events is 0. P(A/B) =P(AB)/P(B) =0/P(B) =0).

d.

P(The subscriber does not complain about incompetent complaint handling nor does the consumer complain about payment disputes) = 1 - P(The subscriber complains about incompetent complaint handling or the consumer complains about payment disputes) =1 - (8% + 11%) =1 - 0.08 - 0.11 =0.81