Question 1181892: The financial 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 late 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 only 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 this customer?
Answer by ikleyn(52825)   (Show Source):
You can put this solution on YOUR website! .
The financial 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 late 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 only 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 this customer?
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They want you calculate the CONDITIONAL probability
P = P(accountant called the customer given that the company received a payment on time from the customer).
According to the definition of the conditional probability, this probability is the ratio of two values
P(accountant called the customer AND the company received a payment on time from the customer)
to
P(company received a payment from the customer).
The denominator is equal to
P(company received a payment from the customer) = 0.6*0.9 + (1-0.6)*0.5 = 0.74.
The numerator is equal to
P(accountant called the customer AND the company received a payment on time from the customer) = 0.6*0.9 = 0.54.
THEREFORE, the conditional probability under the problem's question is
P =  =  =  = 0.72972973... = 0.7297 (rounded) = 72.97%. ANSWER
Solved, answered and carefully explained.
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On conditional probability, see the lessons
- Conditional probability problems
- Conditional probability problems REVISITED
in this site.
Read them to develop your skills and knowledge.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Solved problems on Probability"
and "Additional problems on Probability".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.
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