### Florida

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.

1. Andy Stedman1:14 PM

25%, 0, 50%.

2. Andy, why does a two-child family with a girl have no chance of another girl? I'm puzzled about your reasoning.

4. I fell for the trick on the third question. What do I know about people who would call a child "Florida?"

5. There's really no trick: the significance of the name Florida is that it is rare, so that girls and girls not named Florida are much the same. This facilitates setting up equiprobable cases of two children, one of whom is a girl named Florida. You end up with four cases, two of which are cases of two girls.

6. I wasn't willing to make the assumption that the sex of the other sibling was independent of the choice of the name Florida. I'm aware that I'm somewhat socially retarded, so for all I knew the name "Florida" was most often bestowed upon the next child after a male birth.

7. Yeah, good point, but such argument to cogent reason basically destroys all nice probabilistic riddles: If you flip a coin and it's heads, and then you flip again, how do I know that--were it tails--you would not be shot and your body dumped at sea so that I would never find out, and furthermore, I'd be shot as well so that I would not be suspicious that the experiment had ended prematurely, all of which would--in such a universe--lead to a judgment that the probability of heads after heads is 100%?

8. scineram11:01 AM

Yeah, (ii) is 1/3.

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