Assume that each born child 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 scenarios given a family has two children, where each child can either be a boy (B) or a girl (G).

### Step 1: Define the Sample Space
The sample space for a family with two children can be represented as:
- GG (both are girls)
- GB (first is a girl, second is a boy)
- BG (first is a boy, second is a girl)
- BB (both are boys)
...