document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=945652>Question 945652</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let the random variable x represent the number of automobiles that a top salesperson will sell to a corporate client. The only possible values for  are 0, 1 and 2, and the probabilities for each of these values may be calculated from the formula <BR>\n" );
document.write( "P(x)=0.5-(x/6)	 where  x=0, 1 or 2<BR>\n" );
document.write( "What is the probability that a randomly selected top salesperson will sell <BR>\n" );
document.write( "		i.	at least 1 automobile to a corporate client?<BR>\n" );
document.write( "		ii.	at most 1 automobile to a corporate client?<BR>\n" );
document.write( "		iii.	exactly 1 automobile to a corporate client?<BR>\n" );
document.write( "&#8195;\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #576850 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=576850\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">   <BR>\n" );
document.write( "Given<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X%29=0.5-%28X%2F6%29 ALIGN=MIDDLE  ALT=\"P%28X%29=0.5-%28X%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with X&isin;{0,1,2}<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Find<BR>\n" );
document.write( "1. P(X&ge;1)<BR>\n" );
document.write( "2. P(X&le;1)<BR>\n" );
document.write( "3. P(1)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Solution<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Using the given probability distribution, we find<BR>\n" );
document.write( "P(0) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5-0%2F6+=+1%2F2 ALIGN=MIDDLE  ALT=\"0.5-0%2F6+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P(1) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5-1%2F6+=+1%2F3 ALIGN=MIDDLE  ALT=\"0.5-1%2F6+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P(2) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5-2%2F6+=+1%2F6 ALIGN=MIDDLE  ALT=\"0.5-2%2F6+=+1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "from which we check &Sigma;P(X)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2%2B1%2F3%2B1%2F6+=+1 ALIGN=MIDDLE  ALT=\"1%2F2%2B1%2F3%2B1%2F6+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > checks.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Since the probabilities are mutually exclusive, we can apply the addition rule:<BR>\n" );
document.write( "1. P(X&ge;1) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281%29%2BP%282%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"P%281%29%2BP%282%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. P(X&le;1) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%280%29%2BP%281%29+=+5%2F6 ALIGN=MIDDLE  ALT=\"P%280%29%2BP%281%29+=+5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3. P(1) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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