document.write( "Question 872245: in your pocket you have a quarters, two dimes, and three pennies. If all amounts are equally likely, what is the probability that you can match the\"change\" part of your bill? ( If the bill were $7.10, thw change part would be the $0.10.) \n" ); document.write( "

Algebra.Com's Answer #526017 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "We can choose the number of quarters to use 2 ways, \r\n" );
document.write( "that is, we can choose to use no quarters, or 1 quarter.\r\n" );
document.write( "That's 2 ways.\r\n" );
document.write( "\r\n" );
document.write( "For each of those 2 choices for the number of quarters,\r\n" );
document.write( "we can choose the number of dimes to use 3 ways, \r\n" );
document.write( "that is, we can choose to use no dimes, 1 dime, or 2 dimes.\r\n" );
document.write( "So we can choose the numbers of quarters and dimes to use\r\n" );
document.write( "in 2×3 or 6 ways.\r\n" );
document.write( "\r\n" );
document.write( "For each of those 2×3 or 6 choices for the number of quarters\r\n" );
document.write( "and dimes to use, we can choose the number of pennies 4 ways, \r\n" );
document.write( "that is, we can choose to use no pennies, 1 penny, 2 pennies,\r\n" );
document.write( "or 3 pennies. So we can choose the numbers of quarters, dimes \r\n" );
document.write( "and pennies to use in 2×3×4 or 24 ways. \r\n" );
document.write( "\r\n" );
document.write( "No two of those 24 combinations of coins will produce the same \r\n" );
document.write( "number of cents, so there are 24 possible numbers of cents \r\n" );
document.write( "we can make with 1 quarter, 2 dimes and 3 pennies. \r\n" );
document.write( "\r\n" );
document.write( "There are 100 different numbers of cents our bill can have, \r\n" );
document.write( "\r\n" );
document.write( ".00, .01, ... .99\r\n" );
document.write( "\r\n" );
document.write( "So the probability that we can match the \"change\" part of \r\n" );
document.write( "our bill is  or . [ 24% of the time\r\n" );
document.write( "we can match the \"change\" and 76% of the time we can't].\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "

\n" );