SOLUTION: 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. (a) The bill is a $5 bill

Question 1120437: 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.
(a) The bill is a $5 bill, given that it is not a $1 bill.
(b) The bill is a $1 bill, given that it is smaller than $10.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

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.

(a) The bill is a $5 bill, given that it is not a $1 bill.

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.

(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.
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