So, I'm going to counter here and say I don't find this to be a good intro. I started reading and had not heard of the "Girl named Florida" problem and then went to the linked to blog post http://allendowney.blogspot.com/2011/11/girl-named-florida-s...
The way he explains it I found to be confusing and counter-intuitive. I've taken basic stats in college, and learned some of the associated problems, though not this one, and learned the material though not in this particular way. I have to agree whole-heartedly with the commenter on that post "JeffJo" who stipulates why it's an ineffectual way to present the material. Furthermore, I found the author's dismissal of the valid criticism to be enough to not want me to read further.
The problem with the Girl Named Florida is that the ambiguous wording is more confusing than the math.
Ambiguous: "In a family with two children, what are the chances, if one of the children is a girl named Florida, that both children are girls?"
More clear, and emphasizing the importance of precise wording when discussing probability: "Among families with two children, with at least one of the children being a girl named Florida, what portion have two girls? (Assume that all names are chosen randomly from the same distribution, independently of all other factors; and sex is determined as by a fair coin toss.)"
I agree that his first example, "The Girl Named Florida" was a confusing example.
I feel pretty comfortable with Bayesian statistics, and I thought the other examples that I saw were pretty clear. But his very first example jumps you out to another webpage, and then he mixes it with "the red-haired problem". It was irritating.
His next example, "The Cookie Problem" is the classic intro-to-Bayes example, IMO.
As someone with nearly zero knowledge of statistics or Bayes' Theorem, I agree: the cookie problem was a very clear example to follow. The "Girl named Florida" solution, while interesting, probably doesn't work as well as a textbook example, at least not in that stage of learning.
Reading the Florida problem solution, it made some sense, but was definitely of a higher level of complexity than the rest of the text.
What I found really interesting was that the answers to some of the other questions on the "Girl Named Florida" discussion required knowledge which I would not have considered general math-ish knowledge:
> If the parents have brown hair
> and one of their children has red hair,
> we know that both parents are heterozygous,
> so their chance of having a red-haired girl is 1/8.
Interesting to learn, but this "if you also happen to know this ..." step is something that was mildly frustrating.
(edit: Since the grandparent post linked the Girl Named Florida blog post, I guess I don't need to.)
Oops, I only cut-and-pasted half of what I wanted. This comes after my other reply.
Yes, these sorts of problems can be confusing. But the confusion is propagated by educators who refuse to recognize that what they asked is not what they intended to ask, and so they provide inconsistent answers.
Say you are on a game show, and pick Door #1. The host opens door #3 to show that it does not have the prize, and offers to let you switch to door #2. Should you? Most people will initially reason that door #3 is prize-less 2/3 of the time, evenly split between cases where the prize is behind door #1 and door #2. So it would be pointless to switch. But that is wrong. Few educators will explain why by solving the problem rigorously. They will use an analogy like pointing out how the original choice is right only 1/3 of the time, and since the host can always open a prize-less door, that can’t change.
People don’t believe these educators because their 1/2 answer is indeed more rigorous than the analogy. It just makes a mistake. The probabilities to use are not the probabilities that the cases exist, but the probabilities that the observed result would occur. The existence probabilities are the same, but the probability of the observed result when the initial door was correct is half of what it is when the initial choice was incorrect.
Yes, these sorts of problems can be confusing. But the confusion is propagated by educators who refuse to recognize that what they asked is not what they intended to ask, and so they provide inconsistent answers.
Say you are on a game show, and pick Door #1. The host opens door #3 to show that it does not have the prize, and offers to let you switch to door #2. Should you? Most people will initially reason that door #3 is prize-less 2/3 of the time, evenly split between cases where the prize is behind door #1 and door #2. So it would be pointless to switch. But that is wrong. Few educators will explain why by solving the problem rigorously. They will use an analogy like pointing out how the original choice is right only 1/3 of the time, and since the host can always open a prize-less door, that can’t change.
People don’t believe these educators because their 1/2 answer is indeed more rigorous than the analogy. It just makes a mistake. The probabilities to use are not the probabilities that the cases exist, but the probabilities that the observed result would occur. The existence probabilities are the same, but the probability of the observed result when the initial door was correct is half of what it is when the initial choice was incorrect.
The way he explains it I found to be confusing and counter-intuitive. I've taken basic stats in college, and learned some of the associated problems, though not this one, and learned the material though not in this particular way. I have to agree whole-heartedly with the commenter on that post "JeffJo" who stipulates why it's an ineffectual way to present the material. Furthermore, I found the author's dismissal of the valid criticism to be enough to not want me to read further.