document.write( "Question 1152183: a two digit number has each of the digits {0, 1, 2, 3, 4, 5, 6} appearing exactly once. what is the probability that the number is divisible by two? \n" ); document.write( "

Algebra.Com's Answer #774138 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r
\n" );
document.write( "\n" );
document.write( "Assuming 01, 02, etc. are considered two digit numbers:\r
\n" );
document.write( "\n" );
document.write( "P(even number formed from random selection of two digits, without replacement) = P(even number chosen for ten's digit AND even number chosen for one's digit) +
\n" );
document.write( "P(odd number chosend for ten's digit AND even number chosen for one's digit)\r
\n" );
document.write( "\n" );
document.write( "= (4/7)(3/6) + (3/7)(4/6)
\n" );
document.write( "=  12/42 + 12/42
\n" );
document.write( "=  24/42
\n" );
document.write( "=  \r
\n" );
document.write( "\n" );
document.write( "This matches the proportion of even digits in the set to the total number of digits in the set.  Coincidence?\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "-----
\n" );
document.write( "Expanding the problem to 3 digit numbers you will find P(even) = 4/7 
\n" );
document.write( "Expanding to 4 digit numbers also gives P(even) = 4/7\r
\n" );
document.write( "\n" );
document.write( "-----
\n" );
document.write( "The above cases assume 0 as a leading digit counts, if 0 is disallowed as a leading digit then for two-digit cases P(even) = (3/7)(3/6)+(3/7)(4/6) = 1/2.
\n" );
document.write( "  \n" );
document.write( "

\n" );