document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=758780>Question 758780</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I calculated a probability that must be incorrect.\r<BR>\n" );
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document.write( "*******  Here is the problem statement:<BR>\n" );
document.write( "Given: You have 100 colored marbles in a bag; 25-Red, 25-Blue, 25-Green & 25-Yellow.<BR>\n" );
document.write( "Problem: What is the probability of drawing 4 marbles (at 1 time) of the same color?\r<BR>\n" );
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document.write( "*******  Here is my solution:<BR>\n" );
document.write( "There are 25-Red + 25-Blue + 25-Green + 25-Yellow = 100 total marbles.<BR>\n" );
document.write( "Draw 4 marbles at a time.\r<BR>\n" );
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document.write( "The possible outcomes = 100C4 = 825\r<BR>\n" );
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document.write( "The number of ways to draw 4-Red marbles out of 25 is 25C4 = 50.<BR>\n" );
document.write( "The number of ways to draw 4-Blue marbles out of 25 is 25C4 = 50.<BR>\n" );
document.write( "The number of ways to draw 4-Green marbles out of 25 is 25C4 = 50.<BR>\n" );
document.write( "The number of ways to draw 4-Yellow marbles out of 25 is 25C4 = 50.\r<BR>\n" );
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document.write( "The total ways you can get 4 of the same colored marbles is 50+50+50+50 = 200\r<BR>\n" );
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document.write( "P(ALL THE SAME COLOR) = 200 / 825 = 24%\r<BR>\n" );
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document.write( "This can't be correct! Can you help me understand the error in my calculation?\r<BR>\n" );
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document.write( "On the other hand, if it's correct, could you explain why it is correct?\r<BR>\n" );
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document.write( "Obviously, I have no confidence in my answer.\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #461660 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20081)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=461660\">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 calculated a probability that must be\r\n" );
document.write( "incorrect. \r\n" );
document.write( "******* Here is the problem statement:\r\n" );
document.write( "Given: You have 100 colored marbles in\r\n" );
document.write( "a bag; 25-Red, 25-Blue, 25-Green & \r\n" );
document.write( "25-Yellow.\r\n" );
document.write( "Problem: What is the probability of\r\n" );
document.write( "drawing 4 marbles (at 1 time) of the\r\n" );
document.write( "same color? \r\n" );
document.write( "******* Here is my solution:\r\n" );
document.write( "There are 25-Red + 25-Blue + 25-Green +\r\n" );
document.write( "25-Yellow = 100 total marbles.\r\n" );
document.write( "Draw 4 marbles at a time. \r\n" );
document.write( "The possible outcomes = 100C4 = 825 \r\n" );
document.write( "<font color=\"red\">No! 100C4 = 3921225\r\n" );
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document.write( "The number of ways to draw 4-Red marbles out of 25 is 25C4 = 50. \r\n" );
document.write( "<font color=\"red\">No! 25C4 = 12650\r\n" );
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document.write( "The number of ways to draw 4-Blue marbles out of 25 is 25C4 = 50. \r\n" );
document.write( "<font color=\"red\">No! 25C4 = 12650\r\n" );
document.write( "</font>\r\n" );
document.write( "The number of ways to draw 4-Green marbles out of 25 is 25C4 = 50. \r\n" );
document.write( "<font color=\"red\">No! 25C4 = 12650\r\n" );
document.write( "</font>\r\n" );
document.write( "The number of ways to draw 4-Yellow marbles out of 25 is 25C4 = 50. \r\n" );
document.write( "<font color=\"red\">No! 25C4 = 12650\r\n" );
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document.write( "The total ways you can get 4 of the same colored marbl\r\n" );
document.write( "es is 50+50+50+50 = 200 \r\n" );
document.write( "<font color=\"red\">No! 12650+12650+12650+12650 = 50600\r\n" );
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document.write( "P(ALL THE SAME COLOR) = 200 / 825 = 24%. \r\n" );
document.write( "<font color=\"red\">No! 50600/3921225\r\n" );
document.write( " = 0.0129041307 = or about 1.29%\r\n" );
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document.write( "You are calculating combinations incorrectly.  If you have a TI-83 or 84,\r\n" );
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document.write( "To calculate 100C4,\r\n" );
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document.write( "Type 100\r\n" );
document.write( "Press MATH\r\n" );
document.write( "Press left arrow key once\r\n" );
document.write( "Press 3\r\n" );
document.write( "Type 4    read 100 nCr 4\r\n" );
document.write( "Press ENTER     read 3921225\r\n" );
document.write( "  \r\n" );
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document.write( "Edwin</PRE> </SPAN>\n" );
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