document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73841>Question 73841</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a pair of dice is rolled, the total will range from 2 (1,1) to 12 (6,6). It is a fact that some numbers will occur more frequently than others as the dice are rolled over and over.\r<BR>\n" );
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document.write( "Why will some numbers come up more frequently than others? <BR>\n" );
document.write( "Each die has six sides numbered from 1 to 6. How many possible ways can a number be rolled? In other words, we can roll (2,3) or (3,2) or (6,1) and so on. What are the total (x,y) outcomes that can occur? <BR>\n" );
document.write( "How might you then estimate the percentage of the time a particular number will come up if the dice are rolled over and over? <BR>\n" );
document.write( "Once these percentages have been calculated, how might the mean value of the all the numbers thrown be determined? <BR>\n" );
document.write( "If you have completed the Discussion Board assignment, you have an idea of what a population distribution is. There is a very famous distribution that describes the frequency of the number of times a number comes up in a series of dice rolls. Use the Library or the Internet to see if you can find its name. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52822 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=52822\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When a pair of dice is rolled, the total will range from 2 (1,1) to 12 (6,6). It is a fact that some numbers will occur more frequently than others as the dice are rolled over and over. <BR>\n" );
document.write( "Why will some numbers come up more frequently than others? <BR>\n" );
document.write( "Because combinations of two die sometimes give few occurrences of some numbers<BR>\n" );
document.write( "and more frequest occurrence of others.<BR>\n" );
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document.write( "Each die has six sides numbered from 1 to 6. How many possible ways can a number be rolled? In other words, we can roll (2,3) or (3,2) or (6,1) and so on.<BR>\n" );
document.write( "2: 1,1<BR>\n" );
document.write( "3: 1,2 or 2,1<BR>\n" );
document.write( "4: 1,3 or 2,4 or 3,1<BR>\n" );
document.write( "5: 1,4 or 2,3 or 3,2, or 4,1<BR>\n" );
document.write( "6: 1,5 or 2,4 or 3,3 or 4,2 or 5,1<BR>\n" );
document.write( "7: 1,6 or 2,5 or 3,4 or 4,3 or 5,2 or 6,1<BR>\n" );
document.write( "etc\r<BR>\n" );
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document.write( " What are the total (x,y) outcomes that can occur? <BR>\n" );
document.write( "6*6 or 36 outcomes<BR>\n" );
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document.write( "How might you then estimate the percentage of the time a particular number will come up if the dice are rolled over and over? <BR>\n" );
document.write( "Divide the number of times a sum can occur by 36<BR>\n" );
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document.write( "Once these percentages have been calculated, how might the mean value of the all the numbers thrown be determined?<BR>\n" );
document.write( "Expected value is the sum of the product of each of the sums with the probability that sum will occur.\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
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