Question

 A banking executive studying the role of trust in creating customer advocates has determined that 44% of banking customers have complete trust, 47% of banking customers have moderate trust, and 9% have minimal orotrust in their primary financial institution. Ofthebanking customers that hae complete trust, 69% are very likely to recommend theirprimary financial institution of the bankingcustomersthathae moderate trust, 19% are very likely to recommend their primary financial institution; and of the banking customers that have minimal or no trust, 4% are very likely to recommend their primary financial institution. Complete parts (a) and (b) below.

A.) Compute the probability that if a customer indicates he or she is very likely to recommend his or her primary financial institution, the banking customer also has complete trust.

B.) Compute the probability that a banking customer is very likely to recommend his or her primary financial institution.

Answer 1

A)

Let C, MD, ML be the events that the customers have complete, moderate and minimal trust respectively.

Let R denotes the event that the banking customer recommend their primary financial institution.

Then P(C) = 0.44, P(MD) = 0.47 and P(ML) = 0.09

P(R | C) = 0.69, P(R | MD) = 0.19, P(R | ML) = 0.04

By law of total probability,

P(R) = P(R | C) P(C) + P(R | MD) * P(MD) +  P(R | ML) * P(ML)

= 0.69 * 0.44 + 0.19 * 0.47 + 0.04 * 0.09 = 0.3965

Probability that if a customer indicates he or she is very likely to recommend his or her primary financial​ institution, the banking customer also has complete trust = P(C | R)

= P(R | C) P(C) / P(R) (By Bayes theorem)

= 0.69 * 0.44 / 0.3965

= 0.7657

B)

Probability that a banking customer is very likely to recommend his or her primary financial institution

= P(R)

= 0.3965 (From part A)