Q: You meet a stranger on the street, and ask how many children he has. He truthfully says two. You ask "Is the older one a girl?" He truthfully says yes. What is the probability that both children are girls? What would the probability be if your second question had been "Is at least one of them a girl?", with the other conditions unchanged?
- S: There are four equally-likely possibilities
1. Girl Girl 2. Girl Boy 3. Boy Girl 4. Boy Boy
If the stranger says "My oldest child is a girl," he has eliminated cases 3 and 4, and in the remaining cases both are girls 1/2 of the time. If the stranger says "At least one of my children is a girl," he has eliminated case 4 only, and in the remaining cases both are girls 1/3 of the time.