You have three $1 bills, four $5 bills, and two $10 bills in your wallet. You select a bill at random. Without replacing the bill, you choose a second bill at random. What is P($10 then $1)?
To find the first probability, you first find the amount of $10 bills and the total amount. Then you can put this into a fraction:
[tex]\frac{2}{9}[/tex]
Now, do the same but for the total amount, be sure to remove 1 because you have not returned the first one picked. Now find the amount of $1 bills too:
[tex]\frac{3}{8}[/tex]
Now you have two fractions of two consecutive events, now just simply multiply the two together:
[tex]\frac{2}{9}[/tex] x [tex]\frac{3}{8}[/tex] = [tex]\frac{6}{72}[/tex]
Now as both numbers are factors of 6, both can be divided by 6 to get a simplified probability:
