Children Probability

I have two children. At least one of them is a boy. What is the probability that both my children are boys? My sister also has two children. The older child is a girl. What is the probability that both her children are girls?

Answer:

The probability that both my children are boys is 1/3. And that mysister's both children are girls is 1/2. There are four possibilities of having two children (with the oldest listed first):
1. (Girl, Girl) 2. (Girl, Boy) 3. (Boy, Girl) 4. (Boy, Boy) As I have at least one boy, there are three possibilities i.e. 2, 3 and 4. And only in one case both are boys. Hence, the required probability is 1/3. Similarly, since my sister's older child is girl, there are just twopossibilities i.e. 1 and 2. And again, only in one case both are girls. Hence, the reqiured probability is 1/2.