document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153818>Question 1153818</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A box contains 9 balls marked 1 to 9. Four balls are drawn in succession<BR>\n" );
document.write( "without replacement. Determine the probability that the four-digit number<BR>\n" );
document.write( "formed is:\r<BR>\n" );
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document.write( "a. even\r<BR>\n" );
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document.write( "b. greater than 5000\r<BR>\n" );
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document.write( "c. an odd number less than 3000 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #776132 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</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=776132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A box contains 9 balls marked 1 to 9. Four balls are drawn in succession<BR>\n" );
document.write( "without replacement. Determine the probability that the four-digit number<BR>\n" );
document.write( "formed is:<BR>\n" );
document.write( "a. even<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( "The 4-digit number is even when the last digit is even. i.e., 2,4,6, or 8.\r\n" );
document.write( "That's 4 ways the last digit could be OUT OF 9 possible ways.\r\n" );
document.write( "\"OUT OF\" means \"OVER\" so 4 OUT OF 9 means a probability of 4/9.</PRE><BR>\n" );
document.write( "b. greater than 5000<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( "The 4-digit number is greater than 5000 when the first digit is 5,6,7,8 or 9.\r\n" );
document.write( "That's 5 ways the first digit could be OUT OF 9 possible ways.\r\n" );
document.write( "\"OUT OF\" means \"OVER\" so 5 OUT OF 9 means a probability of 5/9.</PRE><BR>\n" );
document.write( "c. an odd number less than 3000<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( "To have a 'successful' 4-digit number, the 1st digit must be 1 or 2 and the 4th\r\n" );
document.write( "digit must be 1,3,5,7 or 9.\r\n" );
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document.write( "Since the first and last digits can't both be 1, we must break the problem\r\n" );
document.write( "down into two cases:\r\n" );
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document.write( "Case 1: The 1st digit is 1 and the last digit is 3,5,7 or 9. \r\n" );
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document.write( "That's 4 ways the 1st and 4th digits can be to have a successful number.\r\n" );
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document.write( "Case 2: The 1st digit is 2 and the last digit is 1,3,5,7,or 9. \r\n" );
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document.write( "That's 5 ways the 1st and 4th digits can be to have a successful number.\r\n" );
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document.write( "That's 4+5 or 9 ways the 1st and 4th digits can be to have a successful 4-digit\r\n" );
document.write( "number.\r\n" );
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document.write( "There are 9∙8 or 72 ways the 1st and 4th digits can be to have either a\r\n" );
document.write( "successful or an unsuccessful number.\r\n" );
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document.write( "That's 9 ways out of 72 or 9/72 which reduces to 1/8.\r\n" );
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document.write( "Edwin</PRE><BR>\n" );
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