document.write( "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? \n" ); document.write( "
Algebra.Com's Answer #811845 by ikleyn(52832)\"\" \"About 
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\n" ); document.write( "The financial director of a hardware wholesaler has asked the accountant to ring each customer five days before
\n" ); document.write( "their account payment is due, as a means of reducing the number of late payments.
\n" ); document.write( "As a result of time constraints, however, only 60% of customers receive such a call from the accountant.
\n" ); document.write( "Of the customers called, 90% pay on time, while only 50% of those not called pay on time.
\n" ); document.write( "The company has just received a payment on time from a customer.
\n" ); document.write( "What is the probability that the accountant called this customer?
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document.write( "They want you calculate the CONDITIONAL probability\r\n" );
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document.write( "    P = P(accountant called the customer given that the company received a payment on time from the customer).\r\n" );
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document.write( "According to the definition of the conditional probability, this probability is the ratio of two values\r\n" );
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document.write( "    P(accountant called the customer AND the company received a payment on time from the customer) \r\n" );
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document.write( "to \r\n" );
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document.write( "    P(company received a payment from the customer).\r\n" );
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document.write( "The denominator is equal to  \r\n" );
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document.write( "    P(company received a payment from the customer) = 0.6*0.9 + (1-0.6)*0.5 = 0.74.\r\n" );
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document.write( "The numerator is equal to\r\n" );
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document.write( "    P(accountant called the customer AND the company received a payment on time from the customer) = 0.6*0.9 = 0.54.\r\n" );
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document.write( "THEREFORE,  the conditional probability under the problem's question is  \r\n" );
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document.write( "    P = \"0.54%2F0.74\" = \"0.27%2F0.37\" = \"27%2F37\" = 0.72972973... = 0.7297  (rounded) = 72.97%.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and carefully explained.\r
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\n" ); document.write( "\n" ); document.write( "On conditional probability,  see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Conditional probability problems \r
\n" ); document.write( "\n" ); document.write( "    - Conditional probability problems REVISITED \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Read them to develop your skills and knowledge.\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic  \"Solved problems on Probability\"
\n" ); document.write( "and  \"Additional problems on Probability\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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\n" ); document.write( "\n" ); document.write( "Do not forget to post your \"THANKS\" to me for my teaching.\r
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