statistics The finance director of a hardware wholesaler has asked the accountan
ID: 3179837 • Letter: S
Question
statistics The finance director of a hardware wholesaler has asked the accountant to ring each customer five days before their account payment is due, as a means of reducing the number of payments. As a result of time constraints, however, only 60% of customers receive such a call from the accountant. Of the customers called, 90% pay on time, while 50% of those not called pay on time. The company has just received a payment on time from a customer. What is the probability that the accountant called the custom?Explanation / Answer
A - probability payment is received
X - probability that the accountant called customer = 0.6
XC - probability that the accountant did not call the customer = 0.4
A/X - proabability that the customer paid on time given the accountant called the customer = 0.9
A/Xc - proabability that the customer paid on time given the accountant didn't call the customer = 0.5
X/A - probability that accountant called customer given that the payment is received
As per Bayes' theorem,
P (X/A) = P(A/X). P(X) / [P(A/X). P(X) + P(A/XC ). P(XC) ]
= 0.9 * 0.6/ [0.9*0.6 + 0.5* 0.4 ]
=0.54/ (0.54+0.20] = 0.54/0.74 = 0.7297
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