document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204905>Question 1204905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A football team has just scored a touchdown. If they go for the extra point kick there is a 94.4% chance <BR>\n" );
document.write( "of success, a 5% chance of a miss and no points, and 0.6% chance of the opponent stopping the play and <BR>\n" );
document.write( "running it back for 2 points (equivalent to losing two points). If they instead go for a two-point<BR>\n" );
document.write( "conversion the chance of success is 47.9%, a 42.1% of missing and no points, and a 10% chance of the <BR>\n" );
document.write( "opponent stopping the play and running it back for 2 points (equivalent to losing two points). What is <BR>\n" );
document.write( "the expected number of points for each choice by the coach and which option should be picked based <BR>\n" );
document.write( "upon the expected points?<BR>\n" );
document.write( "Expected Points for Extra Point Kick: __________<BR>\n" );
document.write( "Expected Points for Two Point Conversion: _________<BR>\n" );
document.write( "The team should pick: <BR>\n" );
document.write( "Cirlce one: Extra point Kick Two Point Conversio </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842264 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=842264\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Expected value for Extra Point Kick = .932<BR>\n" );
document.write( "Expected value for Two Point Conversion = .758<BR>\n" );
document.write( "The team should pick extra point.\r<BR>\n" );
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document.write( "here's why:\r<BR>\n" );
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document.write( "extra point is 1 and opposite team running it back for 2 points is -2.<BR>\n" );
document.write( "you get .944 * 1 + .05 * 0 + .006 * -2 = .932<BR>\n" );
document.write( "2 point conversion is 2 and opposite team running it back for 2 points is -2.<BR>\n" );
document.write( "you get .479 * 2 + .421 * 0 + .1 * -2 = .758\r<BR>\n" );
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document.write( "the expected value is the average number of points per play for each type of attempt.\r<BR>\n" );
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document.write( "assume 1000 attempts at each type of play.\r<BR>\n" );
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document.write( "for the extra point, you get (.944 * 1000 * 1) + (.05 * 1000 * 0) + (.006 * 1000 * -2) = (944 * 1) + (50 * 0) + (6 * -2) = 944 + 0 - 12 = 932 points / 1000 = an average of .932 points per attempt.\r<BR>\n" );
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document.write( "for the 2 point conversion, you get (.479 * 1000 * 2) + (.421 * 1000 * 0) + (.1 * 1000 * -2) = (479 * 2) + (421 * 0) + (100 * * -2) = 958 + 0 - 200 = 758 points  / 1000 = an average of .758 points per attempt.\r<BR>\n" );
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document.write( "the decision based on the statistics favors going for the extra point.\r<BR>\n" );
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document.write( "the decision, however, is based on other considerations as well.<BR>\n" );
document.write( "one consideration is:<BR>\n" );
document.write( "if they go for the extra point and get it, but the other team is 2 points ahead and the game is over after the play, then going for the extra point is useless because they'll lose the game anyway.  <BR>\n" );
document.write( "they have to go for the 2 point conversion just to tie the score and force the game into overtime, even if the probability of success is less than going for the extra point.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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