document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=547249>Question 547249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A game of chance involves spinning a wheel that has 4 equally likely areas to land on. Red, blue, green and white. If paul plays the game 5 times, what is the probability he wins 3 or fewer times? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #356314 by </B><A HREF=/tutors/aboutme.mpl?userid=mathie123><B>mathie123(224)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathie123><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=356314\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We need to know how Paul wins to answer this question, but let's just assume he wins if it lands on red, and hopefully this helps.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since the wheel is equally likely to land on any of the 4 areas, the probability that it lands on red is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (as is the probability of each of the other areas).\r<BR>\n" );
document.write( "\n" );
document.write( "The probability that Paul wins 3 times is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%2A%281%2F4%29%2A%281%2F4%29%2A%283%2F4%29%2A%283%2F4%29=9%2F1024 ALIGN=MIDDLE  ALT=\"%281%2F4%29%2A%281%2F4%29%2A%281%2F4%29%2A%283%2F4%29%2A%283%2F4%29=9%2F1024\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(Note: we are using the product rule (the \"or\" rule), and also note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the probability that the wheel will not land on red).\r<BR>\n" );
document.write( "\n" );
document.write( "Similarly,<BR>\n" );
document.write( " <BR>\n" );
document.write( "The probability that Paul wins 2 times is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%2A%281%2F4%29%2A%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29=27%2F1024 ALIGN=MIDDLE  ALT=\"%281%2F4%29%2A%281%2F4%29%2A%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29=27%2F1024\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The probability that Paul wins 1 times is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%2A%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29=81%2F1024 ALIGN=MIDDLE  ALT=\"%281%2F4%29%2A%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29=81%2F1024\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "And \r<BR>\n" );
document.write( "\n" );
document.write( "The probability that Paul wins  times is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29=243%2F1024 ALIGN=MIDDLE  ALT=\"%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29=243%2F1024\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now the probability that Paul wins 3 or fewer times we can get by using the sum rule and adding each of these individual probabilities.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F1024%2B27%2F1024%2B81%2F1024%2B243%2F1024=360%2F1024=45%2F128 ALIGN=MIDDLE  ALT=\"9%2F1024%2B27%2F1024%2B81%2F1024%2B243%2F1024=360%2F1024=45%2F128\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );