document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1152116>Question 1152116</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A radio station has a contest in which contestants toll a regular 6-sided die. If he rolls a 1 or 2, he wins $50. If he rolls a 3 or a 4, he wins $100. If he rolls a 5, he wins $1000. If he rolls a 6, he doesn't win anything. What is the probability that out of the first 5 contestants exactly 2 win $100? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #774093 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=774093\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "P(win $100) = 2/6 = 1/3  [win $100 with either a 3 or a 4]<BR>\n" );
document.write( "P(other outcome (\"lose\")) = 2/3<br><BR>\n" );
document.write( "The \"probability vector\" for each roll is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29W%2B%282%2F3%29L ALIGN=MIDDLE  ALT=\"%281%2F3%29W%2B%282%2F3%29L\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [1/3 chance of \"winning\" (W); 2/3 chance of \"losing\" (L)]<br><BR>\n" );
document.write( "The probability that exactly 2 out of 5 contestants win $100 is the coefficient of the \"(W^2)(L^3)\" term in the expansion of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2F3%29W%2B%282%2F3%29L%29%5E5 ALIGN=MIDDLE  ALT=\"%28%281%2F3%29W%2B%282%2F3%29L%29%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Expand using the binomial theorem.  The coefficient of the (W^2)(Y^3) term is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C%285%2C2%29%29%2A%281%2F3%29%5E2%2A%282%2F3%29%5E3+=+%2810%29%281%2F9%29%288%2F27%29+=+80%2F243 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.3292181 to 7 decimal places.<br><BR>\n" );
document.write( "If you have a TI83 calculator, you can confirm that result with<br><BR>\n" );
document.write( "2nd-VARS<BR>\n" );
document.write( "binompdf(5,1/3,2) [5 trials; 1/3 probability of winning; 2 successes]<br> </SPAN>\n" );
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