document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200590>Question 1200590</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A pair of symmetrical six-sided dice is rolled. If the sum equals k on the face up, player A wins and the game ends. If the sum is equal to m, B wins and there is no further betting. What is the probability that A wins after n rolls? What is the probability that B will win? ([n, k, m] = [17, 3, 6]) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834763 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=834763\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A pair of symmetrical six-sided dice is rolled. <BR>\n" );
document.write( "If the sum equals k on the face up, player A wins and the game ends. <BR>\n" );
document.write( "If the sum is equal to m, B wins and there is no further betting. <BR>\n" );
document.write( "(a) What is the probability that A wins after n rolls? <BR>\n" );
document.write( "(b) What is the probability that B will win? <BR>\n" );
document.write( "([n, k, m] = [17, 3, 6])<BR>\n" );
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document.write( "(a)  With the given data, the condition that A wins after n= 17 rolls is \r\n" );
document.write( "     that in previous 16 rolls the sum is NEITHER 3 NOR 6, but in the 17th roll the sum is 3.\r\n" );
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document.write( "     The probability to get the sum 3 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F36 ALIGN=MIDDLE  ALT=\"2%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F18 ALIGN=MIDDLE  ALT=\"1%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "     The probability to get the sum 6 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F36 ALIGN=MIDDLE  ALT=\"5%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "     The probability do not have the sum 3 or 6 is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2836-2-5%29%2F36 ALIGN=MIDDLE  ALT=\"%2836-2-5%29%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29%2F36 ALIGN=MIDDLE  ALT=\"29%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "     Thus the probability that A wins after 17 rolls is\r\n" );
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document.write( "          P = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2829%2F36%29%5E16%2A%281%2F18%29 ALIGN=MIDDLE  ALT=\"%2829%2F36%29%5E16%2A%281%2F18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.001747 (rounded).    <U>ANSWER</U>\r\n" );
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document.write( "Part (a) is complete.\r<BR>\n" );
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document.write( "Regarding part (b), the question (b) is unclear to me.\r<BR>\n" );
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document.write( "From the context, I can think that the question asks about the n=17th roll.\r<BR>\n" );
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document.write( "But I also may think that the question does not mean a concrete value of n.\r<BR>\n" );
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document.write( "My advise to you is NEVER put more than one question per post,\r<BR>\n" );
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document.write( "or, at least, to take care that your post and your questions are not ambiguous.\r<BR>\n" );
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document.write( "On rolling dice problems see the lesson\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Rolling-a-pair-of-fair-dice.lesson>Rolling a pair of fair dice</A> \r<BR>\n" );
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document.write( "in this site. &nbsp;You will find there many similar solved problems.\r<BR>\n" );
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document.write( "Read it and learn the subject from there.  &nbsp;After that, &nbsp;you will be able easy solve such problems<BR>\n" );
document.write( "ON &nbsp;YOUR &nbsp;OWN, &nbsp;which is your &nbsp;MAJOR &nbsp;GOAL &nbsp;visiting this forum &nbsp;(I believe).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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