document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1094875>Question 1094875</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A four sided die is rolled. If the outcome is \"1\" or \"2\", you roll once more; otherwise you stop. What is the probability that the sum of rolls is >= 4? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #709469 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1810)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><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=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=709469\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "I'm thinking that's wrong and that you should make a probability \r\n" );
document.write( "tree diagram of all possible outcomes, with the probability of \r\n" );
document.write( "going along each branch (line) written on the branch:\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28800%2C300%2C-1%2C15%2C-1%2C10%2C%0D%0A%0D%0Agreen%28line%286%2C-.75%2C10%2C-.75%29%29%2Cgreen%28line%286%2C-.75%2B1.25%2C10%2C-.75%2B1.25%29%29%2C%0D%0A%0D%0Alocate%2810.8%2C8.9%2Csum=2%29%2C+locate%2810.8%2C7.9%2Csum=3%29%2Clocate%2810.8%2C6.8%2Csum=highlight%284%29%29%2Clocate%2810.8%2C5.9%2Csum=highlight%285%29%29%2Clocate%2810.8%2C4.9%2Csum=3%29%2Clocate%2810.8%2C3.9%2Csum=highlight%284%29%29%2Clocate%2810.8%2C2.8%2Csum=highlight%285%29%29%2Clocate%2810.8%2C1.7%2Csum=highlight%286%29%29%2Clocate%2810.8%2C.9%2Csum=3%29%2Clocate%2810.8%2C-.35%2Csum=highlight%284%29%29%2C+%0D%0A%0D%0Aline%280%2C4%2C5%2C6.5%29%2Cline%280%2C4%2C5%2C3%29%2Cline%280%2C4%2C5%2C.5%29%2Cline%280%2C4%2C5%2C-.5%29%2C%0D%0Aline%286%2C7%2C10%2C8.5%29%2Cline%286%2C7%2C10%2C7.5%29%2Cline%286%2C7%2C10%2C6.5%29%2C+line%286%2C7%2C10%2C5.5%29%2C%0D%0Aline%286%2C3%2C10%2C4.5%29%2Cline%286%2C3%2C10%2C3.5%29%2Cline%286%2C3%2C10%2C2.5%29%2Cline%286%2C3%2C10%2C1.5%29%2C%0D%0A%0D%0Alocate%285.3%2C7.1%2C1%29%2C+locate%285.3%2C3.3%2C2%29%2C+locate%285.3%2C.8%2C3%29%2Clocate%285.3%2C.8-1.2%2C4%29%2C%0D%0Alocate%2810.2%2C8.9%2C1%29%2C+locate%2810.2%2C7.9%2C2%29%2Clocate%2810.2%2C6.8%2C3%29%2Clocate%2810.2%2C5.9%2C4%29%2C%0D%0Alocate%2810.2%2C4.9%2C1%29%2C+locate%2810.2%2C3.9%2C2%29%2C+locate%2810.2%2C2.8%2C3%29%2C+locate%2810.2%2C1.7%2C4%29%2C%0D%0A%0D%0Alocate%282.3%2C6%2C%221%2F4%22%29%2Clocate%282.6%2C4%2C%221%2F4%22%29%2C%0D%0Alocate%282.8%2C2.5%2C%221%2F4%22%29%2Clocate%283.6%2C1.3%2C%221%2F4%22%29%2C%0D%0Alocate%288.3%2C8.6%2C%221%2F4%22%29%2Clocate%288.3%2C7.9%2C%221%2F4%22%29%2C%0D%0Alocate%288.3%2C7.3%2C%221%2F4%22%29%2Clocate%288.3%2C6.6%2C%221%2F4%22%29%2C%0D%0Alocate%28-.7%2C4.3%2CSTART%29%2C+%0D%0A%0D%0Alocate%288.3%2C8.6-4%2C%221%2F4%22%29%2Clocate%288.3%2C7.9-4%2C%221%2F4%22%29%2C%0D%0Alocate%288.3%2C7.3-4%2C%221%2F4%22%29%2Clocate%288.3%2C6.6-4%2C%221%2F4%22%29+%0D%0A%0D%0A%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "The successful outcomes are boxed in red.\r\n" );
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document.write( "The probability of getting the highest highlighted 4 on the \r\n" );
document.write( "right is to go along the branch from START to 1 (roll 1 first),\r\n" );
document.write( "with probability 1/4, and then go along the branch from 1 to \r\n" );
document.write( "the 4 (roll 4 second), with another probability of 1/4.  So\r\n" );
document.write( "the probability of getting the 4 by rolling a 1 first and then\r\n" );
document.write( "a 4, is gotten by multiplying the 1/4 to go from START to 1, times\r\n" );
document.write( "the 1/4 to go from the 1 to the 4. It is similar for the other \r\n" );
document.write( "outcomes on the far right\r\n" );
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document.write( "So \r\n" );
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document.write( "the probability of the upper highlighted 4 is (1/4)(1/4) = 1/16.\r\n" );
document.write( "the probability of the upper highlighted 5 is (1/4)(1/4) = 1/16.\r\n" );
document.write( "the probability of the other highlighted 4 is (1/4)(1/4) = 1/16.\r\n" );
document.write( "the probability of the other highlighted 5 is (1/4)(1/4) = 1/16.\r\n" );
document.write( "the probability of the highlighted 6 is (1/4)(1/4) = 1/16.\r\n" );
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document.write( "plus\r\n" );
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document.write( "the probability of the highlighted 4 on the bottom, the case where\r\n" );
document.write( "a 4 was rolled first and then you stopped is 1/4, so the desired\r\n" );
document.write( "probability is the sum of all those probabilities:\r\n" );
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document.write( "1/16 + 1/16 + 1/16 + 1/6 + 1/16 + 1/4 = 9/16.\r\n" );
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document.write( "Edwin</PRE><BR>\n" );
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