The author of this quiz seems to have completely misunderstood the relevant research. Either he has to assume that all individuals are identical (in which case, the little story is irrelevant) or he needs to apply Bayes rule according to the probabilities associated with the factors expressed in the personality exposition.
Either way, the article's explanation for that particular question is wrong.
Exactly. Here's the example used in Kahneman's book:
"Dick is a 30-year-old man. He is married with no children. A man of high ability and high motivation, he promises to be quite successful in his field. He is well liked by his colleagues.
This description was intended to convey no information relevant to the question of whether Dick is an engineer or a lawyer."
Yes, there's more to it. The experiment was done with 70/30 and 30/70 ratios for different subjects. The book doesn't say whether they specified they were all males, my guess would be that they did.
a frequentist would take issue with the two sons, one born on a tuesday problem. you can actually count up the permutations.
let's say we have 10 engineers, 9 of them are male. we also have 10 lawyers, 6 of them are male. Let's say one in 10 people likes doing math on the weekend.
There are 90 out of 100 ways to have a group of male engineers, one of which who likes math, but only 60 out of 100 ways to do the same with a male lawyer. furthermore, if we add in the four kids as another 1 in 10 thing, the situation gets even worse. This isn't bayesian, this is just counting boxes on a permutation table.
> This isn't bayesian, this is just counting boxes on a permutation table.
It's the same thing. Bayes' theorem allows you to shortcut straight to the answer without having to draw out a full probability tree / permutation table. But the underlying math is the same - in each case you have a different probability of B given A, versus B given (not A).
Personally I wouldn't call it "Bayesian" so much as just "a conditional probability." The question doesn't ask what the probability is that a randomly selected participant is an engineer, it asks what the probability is that a participant is an engineer given that he has "typical" engineer-like traits.
But then yes, ideally you could use Bayes' Rule to find that probability.
Either way, the article's explanation for that particular question is wrong.