document.write( "Question 267453: Three integers are randomly selected without replacement from the set { 1,2,3,5,6,7}. What is the probability that the mean of the values chosen is less than, but not equal to, 5? \n" ); document.write( "

Algebra.Com's Answer #196292 by Edwin McCravy(20063) $\"\"$ $\"About$

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{1,2,3,5,6,7}
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document.write( "To have a mean of less than 5, the three numbers chosen must have\r\n" );
document.write( "a sum less than 15.  \r\n" );
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document.write( "Let's go for the probability of the complement event, that is,\r\n" );
document.write( "the choices of three numbers from the set that will have a sum \r\n" );
document.write( "of 15 or more. Then we will subtract that probability from from 1.\r\n" );
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document.write( "To have a sum that large, the 7 must be chosen, since 6+5+3 is only\r\n" );
document.write( "14.\r\n" );
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document.write( "If the 7 and 6 are chosen, the third choice could be 2,3, or 5.  That's\r\n" );
document.write( "3 ways.\r\n" );
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document.write( "If the largest two chosen are 7 and 5, then only the 3 could be chosen.\r\n" );
document.write( "That's 1 more way.\r\n" );
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document.write( "So there are only 3+1 or 4 choices of three that have a sum of 15 or greater.\r\n" );
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document.write( "There are 6C3 = 20 possible choices, so the probability of the sum being\r\n" );
document.write( "15 or more is 4/20 or 1/5.\r\n" );
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document.write( "Therefore the answer to the given problem is \r\n" );
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document.write( "Edwin

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