document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=518919>Question 518919</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Pls help me solve this question\r<BR>\n" );
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document.write( "A and B play the following game.They throw alternatively a pair of dice.Whosoever gets sum of two numbers on the top as 7 wins the game and the game stops.Suppose A starts the game,find the probability that\r<BR>\n" );
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document.write( "a)A wins the game<BR>\n" );
document.write( "b)B wins the game </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #345415 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=345415\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability of getting a 7 on two dice is 1/6.\r<BR>\n" );
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document.write( "The probability that A wins right away is 1/6. Hence, the probability that B wins right away is (5/6)(1/6) = 5/36. \r<BR>\n" );
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document.write( "The probability that A wins on his second throw is (5/6)(5/6)(1/6) = 25/216. Hence, the probability that B wins on his second throw is (5/6)(5/6)(5/6)(1/6) = 125/1296.\r<BR>\n" );
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document.write( "We repeat this pattern to obtain\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE P(A) = \sum_{i=0}^{\infty} \frac{5^{2k}}{6^{2k+1}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE = \frac{1}{6}\sum_{i=0}^{\infty} \frac{5^{2k}}{6^{2k}} = \frac{1}{6}\sum_{i=0}^{\infty} (\frac{25}{36})^k\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE = (\frac{1}{6})(\frac{1}{1 - \frac{25}{36}}) = \frac{6}{11}\">\r<BR>\n" );
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document.write( "Therefore, the probability that A wins is 6/11, and the probability that B wins is 1 - (6/11), or 5/11. </SPAN>\n" );
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