### Fun with conditional probability

Apr. 9th, 2008 06:21 pm1. A friend mentions that they have two kids. With no other information, what are the odds that they have (a) two boys, (b) one boy and one girl, or (c) two girls? (For the sake of these problems, assume that half of children are boys, half are girls, and people don't have a natural tendency to children of one sex or the other.)

2. Looking at one of their many bookshelves, you spot a Saddle Club book, which (applying gender stereotypes) you may take as indication that

*at least*one of their children is a girl. Based on this information, what are the odds that they have (a) one boy and one girl, or (b) two girls?

3. You mention the Saddle Club book to your friend. He replies "Yeah, that's Mary's." What are the odds that both their kids are girls?

4. As above, but the reply is "Yeah, that's Mary's, she's my eldest."

5. Different friend, same dilemma - two kids, you don't recall their sexes. Being sneaky, you ask "Would your oldest like to come to my kid's birthday party?" and the response is "Yes, she'd love to." What are the odds that both their kids are girls?

6. As above, but the response is "Mary? Yes, she'd love to."

7. You find a Saddle Club book lying on the ground, inscribed 'To Mary'. You ask around the local schools and in a flagrant breach of privacy they give you the addresses of several dozen Saddle-Club-age 'Mary's in the neighbourhood. You go to the first house on the list and, by examining shoes again, deduce that the family has two children. What are the odds that both are girls?

*Which was surprisingly difficult to do - it's actually very hard to convey no more and no less information than one means to when writing these things.