To solve this problem, we can use a tree diagram to illustrate the possible combinations of children. Since each child can either be a boy (B) or a girl (G) and the outcomes are equally likely, the tree for two children would look as follows:
First Child
/ \
B G
/ \ / \
B G B G
This leads to the following possible outcomes for two children:
- BB (first child is a boy, second child is a boy)
- BG (first child is a boy, second child is a girl)
- GB (first child is a girl, second child is a boy)
- GG (first child is a girl, second child is a girl)
However, we are given the condition that the first child is a boy. This means we can eliminate the outcomes involving a girl as the first child (GB and GG). This leaves us with the following outcomes:
- BB (first is a boy, second is a boy)
- BG (first is a boy, second is a girl)
Now we need to find the probability that the second child is a girl given that the first child is a boy. We have two remaining possibilities (BB and BG), where one of them includes the second child being a girl (BG).
Thus, the probability that the second child is a girl given that the first child is a boy is:
- Number of favorable outcomes (BG) = 1
- Total possible outcomes (BB, BG) = 2
The probability is therefore:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{2} \]
Thus, the answer is:
Start Fraction 1 over 2 End Fraction