### Home > CCG > Chapter 4 > Lesson 4.2.1 > Problem4-58

4-58.

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?

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

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

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

$\frac{9}{19}$

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.

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