document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120437>Question 1120437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A wallet contains seven $1 bills, two $5 bills, and five $10 bills. A bill is selected at random from the wallet. Find the probability of the following. <BR>\n" );
document.write( "(a) The bill is a $5 bill, given that it is not a $1 bill.\r<BR>\n" );
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document.write( "(b) The bill is a $1 bill, given that it is smaller than $10. </SPAN>\n" );
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document.write( "With conditional probability, the \"given that\" condition sets the size of the sample space.  I find it much easier to work conditional probability problems using that concept, rather than the formal mathematical definition of conditional probability.<br><BR>\n" );
document.write( "(a) The bill is a $5 bill, given that it is not a $1 bill.<br><BR>\n" );
document.write( "The condition that it is not a $1 bill leaves 2 $5 bills and 5 $10 bills.  So the size of the sample space (the denominator of the probability fraction) is 2+5=7.  2 of those 7 bills are $5 bills, so the probability is 2/7.<br><BR>\n" );
document.write( "(b) The bill is smaller than $10, so it is either a $1 bill or a $5 bill.  The size of the sample space is 7+2=9; 7 of the 9 are $1 bills, so the probability is 7/9. </SPAN>\n" );
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