the jones family has eight children, all of whom are girls. what is the chance that the next child will be a boy?

It doesn't matter how many girls or boys they already have. Simply focus on what you want next. It's a 50/50 chance. So the probability for a boy is 1/2. Same thing if it's a girl.

1/2

Explanation:

We assume that boys and girls are equally likely and that having a boy or girl previously has no influence on the gender of the next child, i. e., births are independent events.

Since the outcomes (boy/girl) are equally likely and that whatever happens prior has no effect on the future outcomes, then we can use coin flipping model in this situation.

So, having a child is like flipping a coin: you can get heads (boys) or tails (girls), and the previous coin flips (genders of previous children) don't influence the next coin flip (gender of the next child).

Using a coin flip model in this situation, you have a 50% chance of your next child being either a boy or girl.