document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83384>Question 83384</A>: <I><SPAN STYLE=\"word-break: break-all;\">  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59893 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=59893\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A single die is rolled. What is the probability of rolling the following:<BR>\n" );
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document.write( "(a) P(4)<BR>\n" );
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document.write( "A single die has 6 numbers on it ... 1, 2, 3, 4, 5, and 6.  Since only one of these<BR>\n" );
document.write( "numbers is 4 and since all six numbers are equally likely to come up, there is one chance<BR>\n" );
document.write( "in 6 that the number will be a 4.  So the answer is <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;\" >. Think of it this way:<BR>\n" );
document.write( "in six rolls of the die you should see each of the 6 likely numbers, one of which will<BR>\n" );
document.write( "be a 4.  So it is 1 chance out of 6 rolls, not 1 out of 5.<BR>\n" );
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document.write( "(b) P(a number greater than 4)<BR>\n" );
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document.write( "On the die there are two numbers greater than 4. (The numbers are 5 and 6). Therefore,<BR>\n" );
document.write( "of the six numbers that can come up, two of them are greater than 4.  So the probability<BR>\n" );
document.write( "of a number greater than 4 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F6 ALIGN=MIDDLE  ALT=\"2%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or 2 out of 6 which is a fraction<BR>\n" );
document.write( "that simplifies <BR>\n" );
document.write( "to <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;\" >. The answer is <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;\" >. <BR>\n" );
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document.write( "You identified the 2 correctly, but you needed to put it over 6, not over 4. On six<BR>\n" );
document.write( "rolls of the die you can get all six numbers, two of which will be the 5 and the 6. So<BR>\n" );
document.write( "the probability is 2 out of 6 rolls which reduces to  <BR>\n" );
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document.write( "(c) P(a number greater than 6) <BR>\n" );
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document.write( "There is no number on the die that is greater than 6.  Therefore, you could roll the die<BR>\n" );
document.write( "forever and you would never see a number greater than 6.  The probability of getting<BR>\n" );
document.write( "a number greater than 6 is zero. (Your answer of 0/6 is OK, but it reduces to just zero.)<BR>\n" );
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document.write( "(d) P(a number less than 7)<BR>\n" );
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document.write( "Every number on the die is less than seven.  Therefore, every roll of the die will produce<BR>\n" );
document.write( "a number less than seven.  You are correct that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F6 ALIGN=MIDDLE  ALT=\"6%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the probability of this <BR>\n" );
document.write( "happening, but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F6 ALIGN=MIDDLE  ALT=\"6%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to 1. So the probability is 1 or 100%.<BR>\n" );
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document.write( "Hope this helps you understand probability a little better. </SPAN>\n" );
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