Greetings! This is from a wonderful book that Gene and Elen turned me on to: Leonard Mlodinow, The Drunkard's Walk (Pantheon Books, 2008). For simplicity, assume that gender in successive children is 50-50 independently for each child.
(i) A family has two children. What is the probability that both are girls?
(ii) A family has two children, one of them a girl. What is the probability that both are girls?
(iii) A family has two children, one of them a girl named Florida. What is the probability that both are girls?
According to the author, Florida was a rather popular name in the first decades of the 20th Century, although it has since been very much in decline.
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