Out of the $20$ contestants in the state math championships, $10$ are girls. For this round, each contestant gets asked one question. The first question goes to a randomly chosen contestant.

1. What is the probability that the first contestant is a girl?

   Hint (a):

   $\frac{\#\text { girls}}{\text {total } \# \text{ of contestants}}$

2. If the first contestant is a girl, what is the probability that the second contestant is a girl?

   Hint (b):

   If the first contestant is a girl, how many girls are left and how many total contestants are left?

   Answer (b):

   $\frac{9}{19}$

3. Is the probability that the second contestant is a girl independent of the first contestant being a girl?

   Hint (c):

   Are your answers to parts (a) and (b) the same or different? What does this indicate about the events?