document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179546>Question 1179546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A market survey shows that 30% of the population used Brand X laundry detergent last year, 8% of the population gave up doing its laundry last year, and 3% of the population used Brand X and then gave up doing laundry last year. Are the events of using Brand X and giving up doing laundry independent? Is a user of Brand X detergent more or less likely to give up doing laundry than a randomly chosen person?\r<BR>\n" );
document.write( "\n" );
document.write( "First, we need to test whether the two events are independent.<BR>\n" );
document.write( "Use X to denote the event described by \"A person used Brand X,\" and G to describe the event \"A person gave up doing laundry.\"<BR>\n" );
document.write( "Recall that the two events are independent if and only if the probability of <BR>\n" );
document.write( "G ∩ X<BR>\n" );
document.write( " is equal to the product of the probabilities of X and of G. That is, if and only if <BR>\n" );
document.write( "P(G ∩ X) = P(G) · P(X).<BR>\n" );
document.write( "To answer the question, calculate P(G), P(X), and <BR>\n" );
document.write( "P(G ∩ X)<BR>\n" );
document.write( " and then compare <BR>\n" );
document.write( "P(G ∩ X)<BR>\n" );
document.write( " to <BR>\n" );
document.write( "P(G) · P(X).<BR>\n" );
document.write( "Because 8% of the population gave up doing laundry, the probability that someone quit doing laundry is <BR>\n" );
document.write( "P(G) = 0.08.<BR>\n" );
document.write( "Similarly, 30% of the population used Brand X, so the probability that someone was a Brand X user is <BR>\n" );
document.write( "P(X) = 0.3<BR>\n" );
document.write( " <BR>\n" );
document.write( "Furthermore, 3% of the population used Brand X and then gave up doing laundry, so the probability that someone was initially a Brand X user and then quit doing laundry is <BR>\n" );
document.write( "P(G ∩ X) = </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #809124 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52802)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=809124\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "See a TWIN problem solved under this link\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "https://www.slader.com/discussion/question/a-market-survey-shows-that-40-of-the-populationused-brand-x-laundry-detergent-last-year-5-of-the-population-gave-up-doing-its-laundry-last-y-e9c21f04/\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Consider it as your TEMPLATE.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Read it attentively.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Having this template in front of you, solve the current problem in the same way, using the same logic.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Be happy and &nbsp;&nbsp;E N J O Y &nbsp;(!)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );