Question

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)?

Answer 1

Greetings!

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:

$\frac{2}{9}$

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:

$\frac{3}{8}$

Now you have two fractions of two consecutive events, now just simply multiply the two together:

$\frac{2}{9}$ x $\frac{3}{8}$ = $\frac{6}{72}$

Now as both numbers are factors of 6, both can be divided by 6 to get a simplified probability:

$\frac{6}{72}$ ÷ 6 = $\frac{1}{12}$

So P($10 then $1) = $\frac{1}{12}$

Hope this helps!