A banking executive studying the role of trust in creating customer advocates has determined that 41 %41% of banking customers have complete trust, 47 %47% of banking customers have moderate trust, and 12 %12% have minimal or no trust in their primary financial institution. Of the banking customers that have complete trust, 66 %66% are very likely to recommend their primary financial institution; of the banking customers that have moderate trust, 16 %16% are very likely to recommend their primary financial institution; and of the banking customers that have minimal or no trust, 1 %1% 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.

A. 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 is 0.78

B. The probability that a banking customer is very likely to recommend his primary financial institution is 0.347

Step-by-step explanation:

A we will use relative probability instead of percentage so every percentage will be divided by 100;

The probability of a customer having complete trust and likely to recommend is: the probability of having complete trust multiplied for the probability of being likely to recommend:

P(A)=0.41*0.66=0.2706

And the probability of any customer recomending the institution is the sum of the probabilities of having complete, some or none trust multiplied by their respective probabilities of recommending:

P(B)=0.41*0.66+0.47*0.16+0.12*0.01=0.347

The probability that if the customer recommened he has complete trust is P(A)/P(B) to normalize the probability:

P(A)/P(B)=0.78