Question

A banking executive studying the role of trust in areating austomer advocates has determined that 42 % of banking customers have complete trust, 48% of banking oustomers have moderate trust, and 10% have minimal or no trust in their primary financial institution. Of the banking oustomers that have complete trust, 68% are very likely to recommerd their primary financial inatution, of the banking oustomers that have moderate trust, 22 % are very likely to recommend their primary financial instluion; and of the benking austomers that have minimal or no trust, 1% are very loly to recemmend their primary financial institution Complete parts (a) and (b) below

 a. Compute the probablity that if a oustomer indicates he or she is very lkely to recommend his or her primary financial insttion, the banking customer also has complete trust 0.728 (Round to three decimal places as needed)

 b. Compute the probablity that a banking oustomer is very likaly to recommend his or her primary financial instution (Round to three decimal places as needed)

Answer 1

Answer :

Given that :

68% people recommended for complete trust = 42% =

22% people recommended for moderate trust = 48% =

1% people recommended for minimal trust = 10% =

a)The probability that if a customer indicates he or she is very likely to recommend his or her primary financial institution,

then banking customer also has complete trust.

i.e P(R/) = P(R ) / P()

= P(R / ) * P()

= 68% * 42%

= 0.68 * 0.42

= 0.2856

P(R/) = 0.2856

B)The probability that a banking customer is very likely to recommend his or her primary financial institution is as follows :

P(R) = P(R / ) * P() + P(R / ) * P() + P(R / ) * P()

= [68% * 42% ]+ [22% * 48%] + [1% * 10%]

=[0.68 * 0.42] + [0.22 * 0.48] + [0.01 * 0.10]

=0.2856 + 0.1056 + 0.01

= 0.3922

P(R) = 0.3922