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 the first contestant is a girl?

   Hint (a):

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

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? Refer to the Math Notes box at the end of Lesson 4.1.5.

   Hint (c):

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