document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166681>Question 1166681</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You roll two six-sided dice. What is the probability that the sum will be odd or a multiple of three? Round your answer to the nearest tenth of a percent. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791215 by </B><A HREF=/tutors/aboutme.mpl?userid=themasterofcircuits><B>themasterofcircuits(27)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=themasterofcircuits><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=themasterofcircuits><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=791215\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let A be the sum is odd<BR>\n" );
document.write( "Let B be the sum is a multiple of three\r<BR>\n" );
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document.write( "P(A or B)=P(A)+P(B)-P(A and B)\r<BR>\n" );
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document.write( "Possible odd sums: 3,5,7,9,11\r<BR>\n" );
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document.write( "3: (1,2) or (2,1)<BR>\n" );
document.write( "5: (1,4), (4,1), (3,2), or (2,3)<BR>\n" );
document.write( "7: (2,5), (5,2), (3,4), (4,3), (6,1), or (1,6)<BR>\n" );
document.write( "9: (3,6), (6,3), (5,4), or (4,5)<BR>\n" );
document.write( "11: (5,6),(6,5)\r<BR>\n" );
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document.write( "This could occur 18 times out of 36 dice roll possibilities.\r<BR>\n" );
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document.write( "So, P(A) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or 0.5 or 50% \r<BR>\n" );
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document.write( "Possible multiples of 3:\r<BR>\n" );
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document.write( "3: (1,2) or (2,1)<BR>\n" );
document.write( "6: (1,5), (5,1), (2,4), (4,2), (3,3)<BR>\n" );
document.write( "9: (3,6), (6,3), (5,4), or (4,5)<BR>\n" );
document.write( "12: (6,6)\r<BR>\n" );
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document.write( "This could occur 12 times out of 36 dice roll possibilities.\r<BR>\n" );
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document.write( "So, P(B) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or 0.33 or 33%\r<BR>\n" );
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document.write( "Now, we need to find the possibilities they have in common. They are:\r<BR>\n" );
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document.write( "3: (1,2) or (2,1)<BR>\n" );
document.write( "9: (3,6), (6,3), (5,4), or (4,5)\r<BR>\n" );
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document.write( "This could occur 6 times out of 36 dice roll possibilities.\r<BR>\n" );
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document.write( "So, P(A and B) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or 0.166 or 16.6%\r<BR>\n" );
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document.write( "Since P(A or B)=P(A)+P(B)-P(A and B):\r<BR>\n" );
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document.write( "P(A or B) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Rounded to the nearest tenth of a percent: P(A or B) = 66.7%<BR>\n" );
document.write( " </SPAN>\n" );
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