document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=322673>Question 322673</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A pair of dice is rolled.  Find the probabilities of the given events.<BR>\n" );
document.write( "a. The sum of four.<BR>\n" );
document.write( "b. The sum of four, given that the sum is odd.<BR>\n" );
document.write( "c. The roll is doubles, given that the sum is four. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #230995 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=230995\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The probability of anything is the number of ways that it can happen that you would consider a success divided by the number of ways it can happen total -- successes and failures.\r<BR>\n" );
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document.write( "There are 36 possible outcomes for rolling a standard pair of 6-sided dice.  Dice with different numbers of sides and with different numbering than the standard 1 through 6 have different numbers of outcomes.\r<BR>\n" );
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document.write( "There are three ways to make a 4.  1,3 2,2 and 3,1.  Hence, the probability of a four is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{3}{36}\ =\ \frac{1}{12}\">.\r<BR>\n" );
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document.write( "Since 4 is an even number there is no combination where the sum is 4 and the sum is odd simultaneously.  The numerator of the fraction is zero.\r<BR>\n" );
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document.write( "There is only one way to roll a 4 with doubles...2 and 2.  That's why they call it the \"hard way\" at the Craps table.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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