A tale of two raffles

Consider the case of a fete at the school of a small town. This town is unusual in that it consists only of 100 2-children families, all of primary school age, 200 children in all. There are 25 boy-boy families, 50 girl-boy families and 25 girl-girl families.

When the families arrive all the boys, all the fathers and the mothers of the boy-boy families go to watch the boys run around outside.

This leaves 100 girls and their 75 mothers inside the hall to play games. They then decide to run two raffles - one for the mums, one for the girls. The rules are the same for each: write your name and either BG or GG on a piece of paper depending on whether your family is a BG or GG family and then place the paper into a bucket - a red one for the mums and a blue one for the girls.

Q1. What is the chance that that a raffle drawn from the red (mum's) bucket will be won by a GG ticket (a GG family)?

A) 50%
B) 33%
C) Something else

Q2. What is the chance that that a raffle drawn from the blue (daughter's) bucket will be won by a GG ticket (a member of a GG family)?

A) 50%
B) 33%
C) Something else

What this example illustrates is that one needs to be careful about identifying what one is counting when judging probabilities in "A Girl Named Florida" problem and ones like it - are you trying to count groups (families) or members of groups (children)?

So, in this example, and considering only the 75 families in the hall, there is a 50% chance that a girl will be member of a family which has 33% likelihood of being a two girl family and this is not a contradiction.