I'm afraid I don't quite understand the point of the second question. Does the answer mean to state authoritatively that that engineers are no more likely to do carpentry and partake in recreational mathematics than lawyers, or is there another explanation?
If it were changed to something like
"2. A team of psychologists performed personality tests on
100 professionals, of which 50 were engineers and 50 were
nurses. Brief descriptions were written for each
subject. The following is a sample of one of the
resulting descriptions:"
"'Jack is a 45-year old man.'"
and if we were to assume that 80% of engineers are men, and that 80% of nurses are women, we'd expect 80% of the men to be engineers (and so expect Jack to be an engineer with 80% probability). Maybe?
Question 4 - the theatre ticket - could be worded more clearly. I thought "as you enter the theatre" meant "as you enter the big room with the stage and lots of chairs". Who would buy a ticket after entering that room, no matter what the circumstance?
The question is really wrong. I've heard a similar question before and it goes more like this:
"A team of psychologists performed personality tests on 100 professionals, of which 5 were engineers and 95 were lawyers. Brief descriptions were written for each subject. The following is a randomly picked sample of one of the resulting descriptions:
'Jack is a 45-year old man who enjoys recreational Mathematics.'
Assume 90% of engineers enjoy recreational Mathematics and only 10% of lawyers do. What is the chance that Jack is an engineer?"
And the point is that the odds are still that Jack is a lawyer. The question as posed in the article, though, really doesn't make sense.
I recently passed (with high distinctions) three postgraduate course exams towards my masters degree (at a top-10 university). Ho hum, don't be impressed; that is not unusual. My strategy, though, is not textbook; I spend more time studying the conceits of the lecturer, than I did the lecture material itself.
With this in mind:
The point we're supposed to accept is that when asked to evaluate the data sets presented, one heuristically makes assumptions based on social norms and crystallised intelligence. I'm pretty sure that this hypothesis was made in the article preceding the quiz, so no excuses for not realising the point of, well, any of the questions.
For the theatre question, I too started with your interpretation. However, it didn't make sense in the context of illustrating the author's hypothesis, so it couldn't have been the "right" answer.
Protip: when considering someone's line of argument in anything but a hard engineering discipline, I usually play the man before the ball - it's much more revealing.
If it were changed to something like
"2. A team of psychologists performed personality tests on 100 professionals, of which 50 were engineers and 50 were nurses. Brief descriptions were written for each subject. The following is a sample of one of the resulting descriptions:"
"'Jack is a 45-year old man.'"
and if we were to assume that 80% of engineers are men, and that 80% of nurses are women, we'd expect 80% of the men to be engineers (and so expect Jack to be an engineer with 80% probability). Maybe?
Question 4 - the theatre ticket - could be worded more clearly. I thought "as you enter the theatre" meant "as you enter the big room with the stage and lots of chairs". Who would buy a ticket after entering that room, no matter what the circumstance?