document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=976608>Question 976608</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a series of 5 games to be played between 2 equally matched teams, the first<BR>\n" );
document.write( "team to win 3 games becomes the champion. Team A has won the first game. The<BR>\n" );
document.write( "probability that team A will be the champion is ?\r<BR>\n" );
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document.write( "Is 3/5 incorrect?<BR>\n" );
document.write( "Since there are 5 games, Team A won the first game. There are 4 more games left. Two more games till Team A wins or three more games till Team B wins. So obviously the probability of Team A winning is higher than Team B winning. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #598189 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=598189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's a chart showing all of the possible combinations and probabilities for a 5 game series. <BR>\n" );
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document.write( "Since each team is equally matched, assume that the chance of A winning a game is 0.5. <BR>\n" );
document.write( "So the probability of each row is just the product of the probabilities. <BR>\n" );
document.write( "A three game series would have a probability of,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=%281%2F2%29%2A%281%2F2%29%2A%281%2F2%29=%281%2F2%29%5E3=1%2F8 ALIGN=MIDDLE  ALT=\"P=%281%2F2%29%2A%281%2F2%29%2A%281%2F2%29=%281%2F2%29%5E3=1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Four game series,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=%281%2F2%29%5E4=1%2F16 ALIGN=MIDDLE  ALT=\"P=%281%2F2%29%5E4=1%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Five game series<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=%281%2F2%29%5E5=1%2F32 ALIGN=MIDDLE  ALT=\"P=%281%2F2%29%5E5=1%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since A already won one game, start in the second column and add up the probabilities of A winning. <BR>\n" );
document.write( "The sum of those probabilities is 0.34375.<BR>\n" );
document.write( "Now this is out of 0.5 instead of 1.0 since half the games have been knocked out since A won the first. <BR>\n" );
document.write( "So the probability of A winning given they won the first is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=0.34375%2F0.5=11%2F16 ALIGN=MIDDLE  ALT=\"P=0.34375%2F0.5=11%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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