Assume that each child born is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that i. the youngest is a girl, ii. at least one is a girl?

Explanation

To solve the problem, we need to find the conditional probabilities for two different scenarios involving a family with two children. We denote girls as 'g' and boys as 'b'. The possible combinations of two children can be represented as follows:

1. gg (both are girls)
2. gb (first is a girl, second is a boy)
3. bg (first is a boy, second is a girl)
4. bb (both are boys)

The sample space (S) is:
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