Question

A banking executive studying the role of trust in creating customer advocates has determined that 44% of banking customers have complete trust, 45% of banking customers have moderate trust, and 11% have minimal or no trust in their primary financial institution. Of the banking customers that have complete trust, 66 % are very likely to recommend their primary financial institution; of the banking customers that have moderate trust, 24% 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 (Round to three decimal places as needed.) 

Answer 1

Let

• Event ct=any given customer has complete trust
• Event mt=any given customer has moderate trust
• Event nt=any given customer has minimal/no trust
• Event R=any given customer is likely to recommend

We know the following probabilities

44% of the customers have complete trust is same as

the probability that any given customer has complete trust is 0.44

P(ct) = 0.44

45% of the customers have moderate trust is same as

the probability that any given customer has moderate trust is 0.45

P(mt) = 0.45

11% of the customers have minimal or no trust is same as

the probability that any given customer has minimal or no trust is 0.11

P(nt) = 0.11

of the banking customers who have complete trust, 66% are likely to recommend is same as

The probability that a customer is likely to recommend given that they have complete trust is 0.66

P(R|ct)=0.66

of the banking customers who have moderate trust, 24% are likely to recommend is same as

The probability that a customer is likely to recommend given that they have moderate trust is 0.24

P(R|mt)=0.24

of the banking customers who have minimal/no trust, 3% are likely to recommend is same as

The probability that a customer is likely to recommend given that they have minimal/no trust is 0.03

P(R|nt)=0.03

a) The probability that if a customer indicates he/she is very likely to recommend, the customer also has complete trust is

ans: 0.723