Question

A purse contains four $\$$5 bills, five $\$$10 bills and three $\$$20 bills. Two bills are selected without the first selection being replaced, find probability of getting both $\$5$ bills.

• A. $\frac{1}{3}$
• B. $\frac{3}{11}$
• C. $\frac{1}{11}$
• D. $\frac{1}{12}$

Answer 1

The correct option is C $\frac{1}{11}$

There are four $\$$5 bills.
There are total of twelve bills.
P($\$$5) $=\frac{4}{12}$

The result of the first draw affected the probability of the second draw.

There are three $\$$5 bills left.
There are a total of eleven bills left.

P($\$$5 after $\$$5) $=\frac{3}{11}$

P($\$$5, then $\$$5)= P($\$$5) $\times$ P($\$$5 after $\$$5) $=\frac{4}{12}\times \frac{3}{11}=\frac{1}{11}$

The probability of drawing a $\$$5 bill and then a $\$$5 bill is $\frac{1}{11}$.