document.write( "Question 444916: How to find the probability of matching 4 out of 5 numbers from a lottery with number 1 to 45 \n" ); document.write( "

Algebra.Com's Answer #306612 by Edwin McCravy(20081) $\"\"$ $\"About$

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How to find the probability of matching 4 out of 5 numbers from a lottery with number 1 to 45
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document.write( "There are 5 numbers that match the winning set and 40 which don't\r\n" );
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document.write( "P(matching exactly 4 and mismatching 1)\r\n" );
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document.write( "The number of ways to choose the 4 matching ones is C(5,4) \r\n" );
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document.write( "For each of those C(5,4) ways to choose the 4 matching ones,\r\n" );
document.write( "there are C(40,1) ways of choosing the nonmatching one.\r\n" );
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document.write( "So there are C(5,4)*C(40,1) ways to choose exactly 4 matching ones\r\n" );
document.write( "and exactly one non-matching one.\r\n" );
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document.write( "There are C(45,5) ways of choosing ANY 5\r\n" );
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document.write( "So the probability is\r\n" );
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document.write( " C(5,4)*C(40,1)       5*40        200\r\n" );
document.write( "---------------- = --------- = --------- = .0001636984053\r\n" );
document.write( "    C(45,5)         1221759     1221759\r\n" );
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document.write( "Not too likely.  Studying math teaches you that gambling \r\n" );
document.write( "without using skill to put the probability of winning in \r\n" );
document.write( "your favor is never wise.\r\n" );
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document.write( "Edwin

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