document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129550>Question 1129550</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question – 7: In each case, determine whether the events E and F are independent or dependent. Justify your answer in each case.\r<BR>\n" );
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document.write( "	7a-)	E: You get a high score on a statistics exam.<BR>\n" );
document.write( "		F: The Boston Bruins win a hockey game.\r<BR>\n" );
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document.write( "	7b-)	E: Your refrigerator works.<BR>\n" );
document.write( "		F: Your television works.<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 #746141 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=746141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "recall:<BR>\n" );
document.write( "Two events are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dependent ALIGN=MIDDLE  ALT=\"dependent\"   DISABLED_style= \"max-width:90%; height:auto;\" > if the occurrence of one of them <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=affects ALIGN=MIDDLE  ALT=\"affects\"   DISABLED_style= \"max-width:90%; height:auto;\" > the probability of the occurrence of the other, but this does not necessarily mean that one of the events is a cause of the other. \r<BR>\n" );
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document.write( "Two events are independent if the occurrence of one <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=does ALIGN=MIDDLE  ALT=\"does\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+not ALIGN=MIDDLE  ALT=\"+not\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+affect ALIGN=MIDDLE  ALT=\"+affect\"   DISABLED_style= \"max-width:90%; height:auto;\" > the probability of the occurrence of the other. \r<BR>\n" );
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document.write( "7a-)	<BR>\n" );
document.write( "E: You get a high score on a statistics exam.<BR>\n" );
document.write( "F: The Boston Bruins win a hockey game. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Independent ALIGN=MIDDLE  ALT=\"Independent\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> E <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=does ALIGN=MIDDLE  ALT=\"does\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+not ALIGN=MIDDLE  ALT=\"+not\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+affect ALIGN=MIDDLE  ALT=\"+affect\"   DISABLED_style= \"max-width:90%; height:auto;\" > the probability of the occurrence of the event F\r<BR>\n" );
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document.write( "7b-)	<BR>\n" );
document.write( "E: Your refrigerator works.<BR>\n" );
document.write( "F: Your television works.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Independent ALIGN=MIDDLE  ALT=\"Independent\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> for same reason as above \r<BR>\n" );
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document.write( " If two events are technically dependent but can be treated as if they are independent according to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >% guideline, consider them to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=independent ALIGN=MIDDLE  ALT=\"independent\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "For example, playing the California lottery and then playing the New York lottery<BR>\n" );
document.write( "are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=independent ALIGN=MIDDLE  ALT=\"independent\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+events ALIGN=MIDDLE  ALT=\"+events\"   DISABLED_style= \"max-width:90%; height:auto;\" > because the result of the California lottery has absolutely<BR>\n" );
document.write( "no effect on the probabilities of the outcomes of the New York lottery.\r<BR>\n" );
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document.write( " In contrast,<BR>\n" );
document.write( "the event of having your car start and the event of getting to your statistics class on time are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dependent ALIGN=MIDDLE  ALT=\"dependent\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=events ALIGN=MIDDLE  ALT=\"events\"   DISABLED_style= \"max-width:90%; height:auto;\" >, because the outcome of trying to start your car does affect the probability of getting to the statistics class on time.\r<BR>\n" );
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