Two Children 2
Previous puzzle in this series
You’re talking to a different colleague at work when it comes up in the conversation that he has 2 children.
“What genders are they?” you ask again.
“Well, the oldest is a girl,” he replies.
What is the probability the family has two daughters?
Hint
You can assume that the probability of any child being a boy or girl to be equal and independent.
Solution
21
When you first find out that your colleague has 2 children, the possibilities made known to you are:
- Both children are boys
- The older child is a boy, and the younger child is a girl
- The older child is a girl, and the younger child is a boy
- Both children are girls
Each outcome comes at equal chance.
This time, knowing the gender of one child does not tell you the gender of the other. Knowing the older child is a girl narrows it down to 2 possibilities (outcomes 3 and 4), only 1 of which involves 2 daughters. Thus, the chances of him having 2 daughters is 21.
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