Answer
1/36
Work Step by Step
You do not replace the coins, so the events are dependent:
P(penny)=$\frac{2}{9}$ -2 of the 9 coins are pennies-
P(quarter after penny)=$\frac{1}{8}$ -1 of the 8 remaining coins are quarters-
Probability:
P( penny then quarter)=P(quarter) $\times$ P( quarter after penny)
P( penny then quarter)=$\frac{2}{9}$ $\times$ $\frac{1}{8}$
P( penny then quarter)=$\frac{1}{36}$