document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110139>Question 1110139</A>: <I><SPAN STYLE=\"word-break: break-all;\"> goliath and David play a game in which there are no ties. Each player is likely to win each game. The first player to win 4 games becomes the champion, and no further games are played. Goliath wins the first 2 games. What is the probability that David becomes the champion? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #725167 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=725167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the probability of winning is 1/2.<BR>\n" );
document.write( "the probability of losing is 1/2.\r<BR>\n" );
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document.write( "david has to win 4 games and can lose at most 1 game in order for david to become the champion.\r<BR>\n" );
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document.write( "in the following table, 1 means a win for david and 0 means a loss for david.\r<BR>\n" );
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document.write( "the probability for a 1 or a 0 is equal to 1/2.\r<BR>\n" );
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document.write( "p(1,1,1,1) = (1/2) ^ 4 = 1/16<BR>\n" );
document.write( "p(1,1,1,0,1) = (1/2)^5 = 1/32<BR>\n" );
document.write( "p(1,1,0,1,1) = (1/2)^5 = 1/32<BR>\n" );
document.write( "p(1,0,1,1,1) = (1/2)^5 = 1/32<BR>\n" );
document.write( "p(0,1,1,1,1) = (1/2)^5 = 1/32\r<BR>\n" );
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document.write( "the probability of david becoming the champion is therefore 1/16 + 4/32 = 6/32 = 3/16.\r<BR>\n" );
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document.write( "in decimal form, that's .1875.\r<BR>\n" );
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document.write( "that's my take.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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