document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184373>Question 1184373</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A & B Pty Ltd manufactures window air-conditioners in both a <BR>\n" );
document.write( "deluxe model and a standard model. An auditor undertaking a <BR>\n" );
document.write( "compliance audit of the firm is validating the sales account for <BR>\n" );
document.write( "April. She has collected 200 invoices for the month, some of which <BR>\n" );
document.write( "were sent to wholesalers and the remainder to retailers. Of the <BR>\n" );
document.write( "140 retail invoices, 28 are for the standard model. Of the <BR>\n" );
document.write( "wholesale invoices, 24 are for the standard model. If the auditor <BR>\n" );
document.write( "selects one invoice at random, find the probability that: <BR>\n" );
document.write( "a) the invoice selected is for the deluxe model .<BR>\n" );
document.write( "b) the invoice selected is wholesale invoice for the deluxe model<BR>\n" );
document.write( "c) the invoice selected is either a wholesale invoice or an invoice <BR>\n" );
document.write( "for the standard model\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849849 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the probabilities:\r<BR>\n" );
document.write( "\n" );
document.write( "First, let's organize the data into a table:\r<BR>\n" );
document.write( "\n" );
document.write( "| Invoice Type | Deluxe Model | Standard Model | Total |<BR>\n" );
document.write( "|---|---|---|---|<BR>\n" );
document.write( "| Retail | 140 - 28 = 112 | 28 | 140 |<BR>\n" );
document.write( "| Wholesale | 200 - 140 - 24 = 36 | 24 | 60 |<BR>\n" );
document.write( "| Total | 112 + 36 = 148 | 28 + 24 = 52 | 200 |\r<BR>\n" );
document.write( "\n" );
document.write( "**a) Probability of a Deluxe Model Invoice:**\r<BR>\n" );
document.write( "\n" );
document.write( "*   There are 148 deluxe model invoices out of a total of 200 invoices.<BR>\n" );
document.write( "*   P(Deluxe) = 148/200 = 0.74 or 74%\r<BR>\n" );
document.write( "\n" );
document.write( "**b) Probability of a Wholesale Invoice for the Deluxe Model:**\r<BR>\n" );
document.write( "\n" );
document.write( "*   There are 36 wholesale invoices for the deluxe model.<BR>\n" );
document.write( "*   P(Wholesale and Deluxe) = 36/200 = 0.18 or 18%\r<BR>\n" );
document.write( "\n" );
document.write( "**c) Probability of a Wholesale Invoice or a Standard Model Invoice:**\r<BR>\n" );
document.write( "\n" );
document.write( "We can use the addition rule for probability:\r<BR>\n" );
document.write( "\n" );
document.write( "P(Wholesale or Standard) = P(Wholesale) + P(Standard) - P(Wholesale and Standard)\r<BR>\n" );
document.write( "\n" );
document.write( "*   P(Wholesale) = 60/200 = 0.30<BR>\n" );
document.write( "*   P(Standard) = 52/200 = 0.26<BR>\n" );
document.write( "*   P(Wholesale and Standard) = 24/200 = 0.12\r<BR>\n" );
document.write( "\n" );
document.write( "P(Wholesale or Standard) = 0.30 + 0.26 - 0.12 = 0.44 or 44%\r<BR>\n" );
document.write( "\n" );
document.write( "Alternatively, we can count the number of invoices that are either wholesale or for the standard model (or both):\r<BR>\n" );
document.write( "\n" );
document.write( "*   Wholesale: 60<BR>\n" );
document.write( "*   Standard: 52<BR>\n" );
document.write( "*   Both: 24\r<BR>\n" );
document.write( "\n" );
document.write( "So, 60 + 52 - 24 = 88 invoices are either wholesale or standard (or both).<BR>\n" );
document.write( "Then P(Wholesale or Standard) = 88/200 = 0.44 or 44%<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );