A couple is planning to have 3 children. Assuming that having a boy and having a girl are equally likely, and that the gender of one child has no influence on (or, is independent of) the gender of another, what is the probability that the couple will have exactly 2 girls?

The "random experiment" in this case is having 3 children, as odd as that may sound in this context. The next and most important step is to determine what all of the possible outcomes are, and list them (i.e., list the sample space S). In this case, each outcome represents a possible combination of genders of 3 children (note that examples with the same number of boys and girls but a different birth order must be listed separately).

1. What is the sample space in this case? (Use B for boy and G for girl).
   
   
   
   
2. Since both genders are equally likely, and since the gender of one child does not affect the gender of another, in this scenario all 8 outcomes are equally likely (each having probability 1/8).
   
   Now we're getting to our event of interest: "Having exactly two girls." Let's denote this event by A.
   
   How many of the 8 outcomes satisfy (or make up) event A? List them.
   
   
   
   
3. We now have all we need in order to find P(A).
   
   What is P(A), the probability of a family with three children having exactly two girls?