document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197527>Question 1197527</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An experiment consists of rolling two fair​ (not weighted) dice and adding the dots on the two sides facing up. Each die has the number 1 on two opposite​ faces, the number 2 on two opposite​ faces, and the number 3 on two opposite faces. Compute the probability of obtaining the indicated sum.<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 #830848 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830848\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The only numbers on the dice are 1, 2, and 3; there are 2 of each number on each die, so the probability of each number on each die is 1/3.  Note the information that the two 1's are on opposite faces, as are the two 2's and the two 3's, is not relevant to the question.<br><BR>\n" );
document.write( "Since the probability of each number on each die is 1/3, the probability of any particular ordered outcome is (1/3)(1/3)=1/9.<br><BR>\n" );
document.write( "Your post did not indicate a particular sum; but since there are not many possible sums it is easy to calculate the probability of each.<br><BR>\n" );
document.write( "sum of 2:<BR>\n" );
document.write( "1+1;  number of outcomes with this sum: 1<BR>\n" );
document.write( "probability(sum of 2) = 1(1/9) = 1/9<BR>\n" );
document.write( "sum of 3:<BR>\n" );
document.write( "1+2 or 2+1;  number of outcomes with this sum: 2<BR>\n" );
document.write( "probability(sum of 3) = 2(1/9) = 2/9<BR>\n" );
document.write( "sum of 4:<BR>\n" );
document.write( "1+3, 2+2, or 3+1;  number of outcomes with this sum: 3<BR>\n" );
document.write( "probability(sum of 4) = 3(1/9) = 3/9 = 1/3<BR>\n" );
document.write( "sum of 5:<BR>\n" );
document.write( "2+3 or 3+2;  number of outcomes with this sum: 2<BR>\n" );
document.write( "probability(sum of 5) = 2(1/9) = 2/9<BR>\n" );
document.write( "sum of 6:<BR>\n" );
document.write( "3+3;  number of outcomes with this sum: 1<BR>\n" );
document.write( "probability(sum of 6) = 1(1/9) = 1/9<br><BR>\n" );
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