document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011646>Question 1011646</A>: <I><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "a)An integer is choosen at random from the first 200 positive integer. what is the probabililty that the integer chosen is divisible by 6  or by 8??\r<BR>\n" );
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document.write( "b)Three horses A,B,C are in a race; A is twice likely to win as B and B is twice as likely to win as C,what is probability that A or B wins??<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627377 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=627377\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "Question:<BR>\n" );
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document.write( "a)An integer is choosen at random from the first 200 positive integer. what is the probabililty that the integer chosen is divisible by 6  or by 8??\r<BR>\n" );
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document.write( "b)Three horses A,B,C are in a race; A is twice likely to win as B and B is twice as likely to win as C,what is probability that A or B wins??<BR>\n" );
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document.write( "Solutions:<BR>\n" );
document.write( "note: floor(x)=[x]=largest integer that does not exceed x.<BR>\n" );
document.write( "a)<BR>\n" );
document.write( "between 1 and 200, <BR>\n" );
document.write( "floor(200/6)=33 are divisible by 6<BR>\n" );
document.write( "floor(200/8)=25 are divisible by 8<BR>\n" );
document.write( "floor(200/24)=8 are divisible by 24 (LCM of 6 and 8)<BR>\n" );
document.write( "So by the inclusion/exclusion principle, (33+25-8)=50 are divisible by 6 or 8.<BR>\n" );
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document.write( "b)<BR>\n" );
document.write( "P(A)=2P(B)<BR>\n" );
document.write( "P(B)=2P(C)<BR>\n" );
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document.write( "P(A)=4P(C)<BR>\n" );
document.write( "or<BR>\n" );
document.write( "P(A)+P(B)+P(C)=(4+2+1)P(C)=7P(C)=1<BR>\n" );
document.write( "P(C)=1/7<BR>\n" );
document.write( "Therefore probability that A or B wins = 1-1/7=6/7\r<BR>\n" );
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