document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328413>Question 328413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Spacecraft are expected to land in a prescribed recovery zone 80% of the time. Over a period of time,six spacecraft land.<BR>\n" );
document.write( "a)Find the probability that none lands in the prescribed zone.<BR>\n" );
document.write( "b)Find the probability that at least one will land in the prescribed zone.<BR>\n" );
document.write( "c)The landing program is called successful if the probability is 0.9 or more that three or more out of six spacecraft will land in the prescribed zone. Is the program successful? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #235274 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=235274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) P(none)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.2%29%5E6=0.000064 ALIGN=MIDDLE  ALT=\"%280.2%29%5E6=0.000064\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "b)At least one means \"not none\".<BR>\n" );
document.write( "P(not none)+P(none)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P(not none)=1-P(none)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-0.000064=0.999936 ALIGN=MIDDLE  ALT=\"1-0.000064=0.999936\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "c) Find P(3 or greater successes)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%283%29%2BP%284%29%2BP%285%29%2BP%286%29 ALIGN=MIDDLE  ALT=\"P%283%29%2BP%284%29%2BP%285%29%2BP%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%280%29=1%2A%280.8%29%5E0%2A%280.2%29%5E6=0.000064 ALIGN=MIDDLE  ALT=\"P%280%29=1%2A%280.8%29%5E0%2A%280.2%29%5E6=0.000064\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281%29=6%2A%280.8%29%5E1%2A%280.2%29%5E5=0.001536 ALIGN=MIDDLE  ALT=\"P%281%29=6%2A%280.8%29%5E1%2A%280.2%29%5E5=0.001536\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%282%29=15%2A%280.8%29%5E2%2A%280.2%29%5E4=0.01536 ALIGN=MIDDLE  ALT=\"P%282%29=15%2A%280.8%29%5E2%2A%280.2%29%5E4=0.01536\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%283%29=20%2A%280.8%29%5E3%2A%280.2%29%5E3=0.08192 ALIGN=MIDDLE  ALT=\"P%283%29=20%2A%280.8%29%5E3%2A%280.2%29%5E3=0.08192\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%284%29=15%2A%280.8%29%5E4%2A%280.2%29%5E2=0.24576 ALIGN=MIDDLE  ALT=\"P%284%29=15%2A%280.8%29%5E4%2A%280.2%29%5E2=0.24576\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%285%29=6%2A%280.8%29%5E5%2A%280.2%29%5E1=0.39322 ALIGN=MIDDLE  ALT=\"P%285%29=6%2A%280.8%29%5E5%2A%280.2%29%5E1=0.39322\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%286%29=1%2A%280.8%29%5E6%2A%280.2%29%5E0=0.26214 ALIGN=MIDDLE  ALT=\"P%286%29=1%2A%280.8%29%5E6%2A%280.2%29%5E0=0.26214\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P(>=3)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%283%29%2BP%284%29%2BP%285%29%2BP%286%29 ALIGN=MIDDLE  ALT=\"P%283%29%2BP%284%29%2BP%285%29%2BP%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P(>=3)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.08192%2B0.24576%2B0.39322%2B0.26214=highlight%280.983%29 ALIGN=MIDDLE  ALT=\"0.08192%2B0.24576%2B0.39322%2B0.26214=highlight%280.983%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%3E0.9 ALIGN=MIDDLE  ALT=\"P%3E0.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, success.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We could have also calculated,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%280%29%2BP%281%29%2BP%282%29=0.000064%2B0.001536%2B0.01536=0.01696 ALIGN=MIDDLE  ALT=\"P%280%29%2BP%281%29%2BP%282%29=0.000064%2B0.001536%2B0.01536=0.01696\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and subtracted from 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=1-P%280%29-P%281%29-P%282%29=1-0.01696=0.983 ALIGN=MIDDLE  ALT=\"P=1-P%280%29-P%281%29-P%282%29=1-0.01696=0.983\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Same answer but saving one step. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );