document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=712389>Question 712389</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A AND B PLAY 12 GAMES OF CHESS,OF WHICH 6 ARE WON BY A,4 BY B AND 2 END IN A TIE.THEY AGREE TO PLAY 3 MORE GAMES.FIND THE PROBABILITY THAT<BR>\n" );
document.write( "a)A WIN ALL THE THREE GAMES<BR>\n" );
document.write( "b)TWO GAMES END IN A TIE<BR>\n" );
document.write( "c)A AND B WIN ALTERNATIVELY AND<BR>\n" );
document.write( "d)B WINS AT LEAST ONE GAME </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #437928 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=437928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A AND B PLAY 12 GAMES OF CHESS,OF WHICH <BR>\n" );
document.write( "6 ARE WON BY A,<BR>\n" );
document.write( "4 BY B AND <BR>\n" );
document.write( "2 END IN A TIE.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P(A win) = 6/12 = 1/2<BR>\n" );
document.write( "P(B win) = 4/12 = 1/3<BR>\n" );
document.write( "P(tie) = 2/12 = 1/6<BR>\n" );
document.write( "-------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "THEY AGREE TO PLAY 3 MORE GAMES.FIND THE PROBABILITY THAT<BR>\n" );
document.write( "a)P(A WIN ALL THE THREE GAMES) = (1/2)^3 = 1/8<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "b)P(TWO GAMES END IN A TIE) = (1/6)^2 = 1/36<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "c)A AND B WIN ALTERNATIVELY <BR>\n" );
document.write( "P(ABA or BAB) = (1/2)^2(1/3) + (1/3)^2(1/2) = 1/12 + 1/18 = (3+2)/36 = 5/36<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "d)P(B WINS AT LEAST ONE GAME) = [P(BB'B')]^3 =[(1/3(1/2)^2]^3 = 1/12^3 <BR>\n" );
document.write( "================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );