document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161724>Question 161724</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A calculator requires a keystroke assembly and a logic circuit. Assume that 88% of the keystroke assemblies and 93% of the logic circuits are satisfactory.\r<BR>\n" );
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document.write( "a. Find the probability that a  finished calculator will be satisfactory\r<BR>\n" );
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document.write( "b. Find the probability that a finished calculator will have both a bad keystroke assembly and a bad logic circuit.\r<BR>\n" );
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document.write( "c. Find the probability that a finished calculator will have either a bad keystroke assembly or a bad logic circuit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119197 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=119197\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a = key stroke assembly is good.<BR>\n" );
document.write( "let b = logic circuit is good<BR>\n" );
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document.write( "p(a) = .88<BR>\n" );
document.write( "p(~a) = 1-.88 = .12<BR>\n" );
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document.write( "p(b) = .93<BR>\n" );
document.write( "p(~b) = .07<BR>\n" );
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document.write( "~a means (not) a means keystroke assembly is bad<BR>\n" );
document.write( "~b means (not) b means logic circuit is bad.<BR>\n" );
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document.write( "a. Find the probability that a  finished calculator will be satisfactory<BR>\n" );
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document.write( "probability finished calculator is good means the keystroke assembly and the logic circuit is good.<BR>\n" );
document.write( "p(a and b) = p(a)*p(b)<BR>\n" );
document.write( "p(a)*p(b) = .88*.93 = .8184<BR>\n" );
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document.write( "b. Find the probability that a finished calculator will have both a bad keystroke assembly and a bad logic circuit.<BR>\n" );
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document.write( "probability that a finished calculator will have both a bad keystroke assembly and a bad logic circuit is p (~a and ~b).<BR>\n" );
document.write( "p(~a and ~b) = p(~a)*p(~b) = .12*.07 = .0084<BR>\n" );
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document.write( "c. Find the probability that a finished calculator will have either a bad keystroke assembly or a bad logic circuit.<BR>\n" );
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document.write( "probability that a finished calculator will have either a bad keystroke assembly or a bad logic circuit is equal to 1 minus the probability that they are both good.<BR>\n" );
document.write( "p(~(a or b)) = 1 - p(a and b)<BR>\n" );
document.write( "p(a and b) = p(a)*p(b) = .8184 (calculated above in part a).<BR>\n" );
document.write( "1 - p(a and b) = 1 - p(a)*p(b) = 1 - .8184 = .1816.<BR>\n" );
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document.write( " </SPAN>\n" );
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