A jar contains quarters (worth $\$ 0.25$ each), nickels (worth $\$ 0.05$ each) and pennies (worth $\$ 0.01$ each). The value of the quarters is $\$ 10.00$. The value of the nickels is $\$ 10.00$. The value of the pennies is $\$ 10.00$. If Judith randomly chooses one coin from the jar, what is the probability that it is a quarter?
(A) $\frac{25}{31}$
(B) $\frac{1}{31}$
(C) $\frac{1}{3}$
(D) $\frac{5}{248}$
(E) $\frac{1}{30}$
The value of all quarters is $\$ 10.00$.

Each quarter has a value of $\$ 0.25$.

There are thus $10 \div 0.25=40$ quarters in the jar.

Similarly, there are $10 \div 0.05=200$ nickels, and $10 \div 0.01=1000$ pennies in the jar.

In total, there are $40+200+1000=1240$ coins in the jar.

The probability that the selected coin is a quarter is $\frac{\text { the number of quarters }}{\text { the total number of coins }}=\frac{40}{1240}=\frac{1}{31}$.

ANswer: (B)