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?
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<pre>
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 = {{{0.54/0.74}}} = {{{0.27/0.37}}} = {{{27/37}}} = 0.72972973... = 0.7297  (rounded) = 72.97%.     <U>ANSWER</U>
</pre>


Solved, answered and carefully explained.



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On conditional probability, &nbsp;see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Conditional-probability-problems.lesson>Conditional probability problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/More-conditional-probability-problems.lesson>Conditional probability problems REVISITED</A> 

in this site.


Read them to develop your skills and knowledge.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Solved problems on Probability</U>" 
and &nbsp;"<U>Additional problems on Probability</U>". 



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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