document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=851626>Question 851626</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a company purchasing department is busy looking at the quality of computers bought by the company. they found that 15% of all new computers screens have to be replaced within 6 months 27% of all new computers must have their screens or mouse replaced within 6 months. given that a computer's mouse was replaced, 10% must also have their screens replaced within 6 months. <BR>\n" );
document.write( "a) what is the probability that a computer's mouse must be replaced within 6 months?<BR>\n" );
document.write( "b) what is the probability that given a computer's screen was replaced, the same computer's mouse will also be replaced within 6 months? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #512914 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=512914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a company purchasing department is busy looking at the quality of computers bought by the company. <BR>\n" );
document.write( "they found that 15% of all new computers screens have to be replaced within 6 months P(screens bad) = 0.15<BR>\n" );
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document.write( "27% of all new computers must have their screens or mouse replaced within 6 months. P(screens OR mouse bad) = 0.27<BR>\n" );
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document.write( "given that a computer's mouse was replaced, 10% must also have their screens replaced within 6 months:: P(screens bad | mouse bad) = 0.10<BR>\n" );
document.write( "Note: P(screens AND mouse bad) = 0.10*P(mouse bad)<BR>\n" );
document.write( "--------------------------------------. <BR>\n" );
document.write( "a) what is the probability that a computer's mouse must be replaced within 6 months?<BR>\n" );
document.write( "Note: Since P(A OR B) = P(A)+P(B)-P(A AND B),<BR>\n" );
document.write( "P(m) = P(m OR s)-P(s)+P(m AND s)\r<BR>\n" );
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document.write( "P(mouse bad) = P(screens OR mouse) + P(screens AND mouse)-P(screen)<BR>\n" );
document.write( "P(mouse bad) = 0.27+0.10(mouse bad)-0.15<BR>\n" );
document.write( "0.90P(mouse bad) = 0.12 <BR>\n" );
document.write( "P(mouse bad) = 2/15<BR>\n" );
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document.write( "b) what is the probability that given a computer's screen was replaced, the same computer's mouse will also be replaced within 6 months?<BR>\n" );
document.write( "P(mouse bad | screen bad) = P(mouse AND screen bad)/P(screen bad) <BR>\n" );
document.write( "= (0.10)(2/15)/0.15 = 0.089<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=================\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );