A banking executive is studying the role of trust in creating customer advocates, and how valuable trust is to the overall banking relationship. Based on study results, the executive has determined that 44% of banking customers have complete trust in their primary financial institution, 49% of banking customers have moderate trust in their primary financial institution, and 7% have minimal or no trust in their primary financial institution. Of the banking customers that have complete trust in their primary financial institution, 68% are very likely to recommend their primary financial institution; of the banking customers that have moderate trust in their primary financial institution, 20% are very likely to recommend their primary financial institution; and of the banking customers that have minimal or no trust in their primary financial institution, 3% are very likely to recommend their primary financial institution. (Data extracted from “Global Consumer Banking Survey-2014,” bit.ly/1gwJJuT.)

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

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