document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=345439>Question 345439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Transportation Safety Authority (TSA) has developed a new test to detect large amounts of liquid in luggage bags. Based on many test runs, the TSA determines that if a bag does contain large amounts of liquid, there is a probability of 0.92 the test will detect it. If a bag does not contain large amounts of liquid, there is a 0.1 probability the test will conclude that it does (a false positive). Suppose that in reality only 3 in 100 bags actually contain large amounts of liquid. \r<BR>\n" );
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document.write( "A)What is the probability a randomly selected bag will have a positive test? Give your answer to four decimal places. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #247520 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=247520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let D=event of detecting large amount of liquid or positive test<BR>\n" );
document.write( "let L=event of bag containing large amounts of liquid<BR>\n" );
document.write( "let S=event of bag containing small amounts of liquid<BR>\n" );
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document.write( "given<BR>\n" );
document.write( "P(D/L)=0.92<BR>\n" );
document.write( "P(D/S)=0.1<BR>\n" );
document.write( "P(L)=3/100=0.03<BR>\n" );
document.write( "Need to find P(D)<BR>\n" );
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document.write( "P(S)=1-P(L)=1-0.03-0.97<BR>\n" );
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document.write( "P(D)=P(D and L)+P(D and S)<BR>\n" );
document.write( "    =P(D/L)*P(L)+P(D/S)*P(S)<BR>\n" );
document.write( "    =0.92*0.03+0.1*0.97<BR>\n" );
document.write( "    =0.0276+0.097=0.1246 </SPAN>\n" );
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