Question

A banking executive studying the role of trust in creating customer advocates has determined that 43 % of banking customers have complete trust, 47 % of banking customers have moderate trust, and 10 % have minimal or no trust in their primary financial institution. Of the banking customers that have complete trust, 65 % are very likely to recommend their primary financial institution; of the banking customers that have moderate trust, 16 % are very likely to recommend their primary financial institution; and of the banking customers that have minimal or no trust, 3 % 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)

from Bayes theorum P( has complete trust given very likely to recommend)

=P( has complete trust and likely to recommend)/P(likely to recommend)

=(0.43*0.65)/(0.43*0.65+0.47*0.16+0.1*0.03)=0.781381

b)

P( very likely to recommend )=P( has complete trust and likely to recommend)+P( hasmoderate trust and likely to recommend)+P( has minimal or no trust and likely to recommend)

=0.43*0.65+0.47*0.16+0.1*0.03 =0.3577