4 people. Yes.
pt could shake hands, he just didn't ask himself the howmany hands he shook, so the number of hands he shook is a parameter we can play with the make the other numbers work.
So there are 4 people:
Nonpareil
ptgatsby
guest1
guest2
The maximum number of hands any of them could shake is 2, the minimum is 0.
Out of these three people:
Nonpareil
guest1
guest2
you need say which one shook hands with 0, which one with 1, and which one with 2. Note, as far as constraints either guest1 or guest2 could have shaken hands with pt, but Nonpareil couldn't have. Also, guest1 did not shake hands with guest2.
I hope it is clearer now.
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield
<-- my brain
Oh, wait... doh!
All right.
In this situation (spoiler):
- If Guest 2 shakes no hands, Non cannot shake her hand either (for a total of 0).
- Non shakes Guest 1's hand and no others. (for a total of 1)
- Guest 1 shakes PT's and Non's hands (for a total of 2)
So for one other couple:
PT: 1
Non: 1
Guest 1: 2
Guest 2: 0
"Hey Capa -- We're only stardust." ~ "Sunshine"
“Pleasure to me is wonder—the unexplored, the unexpected, the thing that is hidden and the changeless thing that lurks behind superficial mutability. To trace the remote in the immediate; the eternal in the ephemeral; the past in the present; the infinite in the finite; these are to me the springs of delight and beauty.” ~ H.P. Lovecraft
No offense taken. You just might be right that familiarity in concrete application breeds better performance. Though I personally suspect it is mostly a case of there being two kinds of people in the world, those who are naturally vaccinated against the (so-called) base rate fallacy, like you (?), pt (Edit: and Santtu ) and the INTP in my class who said he knew to use Bayes' Rule but didn't bother doing the math in his head, and the rest of us. (And of course the first group would be more prone to end up in work requiring said application.)
Unfortunately I don't remember, but I don't think so.The 12% answer is an example of using an intermediate number as the answer it self. Were 17% and 29% also common incorrect answers?
A great element of the class I attended consisted in the stories the professor (who is a cutting edge researcher in this field) could and did tell of top economists who themselves have committed the various fallacies that they refused to believe that people (like, vox populi - never mind the mathematically literate elite) are capable of committing systematically. His bemusement ended up being infectious (once we had recovered from swallowing the egos he had proven to be irrational, that is ).I found that funny also. But I think that has to do with the style of probability education received by those PHDs. Some times people just learn mechanisms without understanding the notions behind them. If people were taught the Long-Run Frequency interpretation of probability, then they would automatically prune the tree to situations they needed, instead of attempting a complcated and error prone application of Bayes' Rule.
But still, I am always amazed when people I think would generally get these types of problems, miss them. So, I probably just shot down my own theory.
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield
"Hey Capa -- We're only stardust." ~ "Sunshine"
“Pleasure to me is wonder—the unexplored, the unexpected, the thing that is hidden and the changeless thing that lurks behind superficial mutability. To trace the remote in the immediate; the eternal in the ephemeral; the past in the present; the infinite in the finite; these are to me the springs of delight and beauty.” ~ H.P. Lovecraft
Same here. In the Wason card problem, I don't see any reasoning for a card other than A, and the Monty Hall problem seems to be a simple 50/50 chance. The only complication I can see is a tell from the host, which isn't addressed. Is it possible that this is a case of lies, damned lies, and statistics?
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield
It just hit me where this might of come from - I did a lot of research into how the base rate fallacy applied to brokers, funds and so forth back when I was into finances.
Likewise, I probably don't have the same degree of critical thinking/familiarity with practical problems to solve the card problem since it's never been something I've used in my life. In thinking about it, I don't think I can come up with a practical analogy to the card problem... The hall problem I've worked with directly before so I can't really say much for sure there.
I suspect this is significantly different than technical and educational goers... I deviate from the norm along the lines of how I learnt it and how I applied it, the two factors that would seem to matter!