document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153828>Question 1153828</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A box obtains 9 balls marked 1 to 9. Four ball are drawn in succession without replacement. Determine the probability that the four-digit number 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" );
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document.write( "A. P(even)<br><BR>\n" );
document.write( "The last ball drawn has to be even.  4 of the 9 balls are even.<br><BR>\n" );
document.write( "P(even) = 4/9<br><BR>\n" );
document.write( "B. P(greater than 5000)<br><BR>\n" );
document.write( "The first ball drawn has to be 5 or greater.  5 of the 9 balls are 5 or greater.<br><BR>\n" );
document.write( "P(greater than 5000) = 5/9<br><BR>\n" );
document.write( "C. P(odd and less than 3000)<br><BR>\n" );
document.write( "We have to separate this into two cases.  The last ball drawn has to be odd; the first has to be either 1 or 2.<br><BR>\n" );
document.write( "If the first ball drawn is the 1 (probability 1/9), then 4 of the remaining 8 balls are odd.<br><BR>\n" );
document.write( "P(odd number with first digit 1) = (1/9)(4/8) = 4/72<br><BR>\n" );
document.write( "If the first ball drawn is the 2 (also probability 1/9), then 5 of the remaining 8 balls are odd.<br><BR>\n" );
document.write( "P(odd number with first digit 2) = (1/9)(5/8) = 5/72<br><BR>\n" );
document.write( "P(odd number less than 3000) = 4/72+5/72 = 9/72 = 1/8<br><BR>\n" );
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