A couple has two children. If the odds of having a boy or girl are equal, and if one of the children is a girl, what is the probability that both are girls?

The problem can be solved using the principles of probability.

Step 1: Identify the total possible outcomes. A couple with two children can have four possible combinations of genders: Boy-Boy (BB), Boy-Girl (BG), Girl-Boy (GB), and Girl-Girl (GG).

Step 2: Identify the favorable outcomes. The problem states that one of the children is a girl. So, we can eliminate the Boy-Boy (BB) combination. This leaves us with three possible combinations: Boy-Girl (BG), Girl-Boy (GB), and Girl-Girl (GG).

Step 3: Identify the desired outcome. The problem asks for the probability that both children are girls. This corresponds to the Girl-Girl (GG) combination.

Step 4: Calculate the probability. The probability of an event is calculated by dividing the number of desired outcomes by the total number of outcomes. In this case, there is 1 desired outcome (GG) and 3 total outcomes (BG, GB, GG).

So, the probability that both children are girls, given that one of them is a girl, is 1/3 or approximately 0.33.