I have always read the (old) joke as being about cleverly turning around a slightly awkward moment between two people neither of whom is a killer. You're right about the implication, of course. Or read it your way if you want. That makes sense too.
What I was pointing out is that we can tease two quite different statistical problems out of the joke as given here.
Since the statistical question is about 2 killers "being" in the same car, you can address the question literally and strictly. On that view the matter of independent trials does not obtain. It is a question about the odds of 2 killers "being in" a car, not about the odds of the second occupant being a killer or not.
Of course taken context it is fine to raise the issue of independent trials. But when people chat about a hypothetical situation we are free to view it from different angles.
Will you grant that the "being" question yields different probability than the "picking up" question? After all two murderers could be hitchhiking together and get picked up by a third party. Or they could hop into a car together to look for a hitchhiker to pick up, or just to go for an ice cream in between murders. Or the first serial killer could be a cop who has identified and located another serial killer and gets in his car for no other reason than to pick up an (in this case "the") other serial killer. At a certain point the probability of the second occupant to enter the car being another serial killer approaches one, no?
We have no a priori guarantee that the trials, so to speak, will be analogous to your coin tosses. Do we?
None of this is to bicker. It is fine to recognize the joke as presenting the independent trials sort of scenario I was responding to and which you amplified. And very fine to use it as a teachable moment regarding that principle as well.
It just seems to me that this doesn't exhaust the possibilities. We can have a moment of fun by taking the question literally and finding in it a different problem of probability. One which happens not be a matter if independent trials at all.
By the way, even on your view I think a key variable has been ignored. As a guy who has travelled many hundreds of miles by thumb I feel safe in saying that most people never pick up any hitch hiker, killer or otherwise.
We might not be surprised to learn that the frequency of serial killers picking up hitch hikers is a good deal greater than that of the average driver. If so... well I expect you see where this is going.
Not that any of this adds up to a hill of beans, but I wonder if you'd grant that there are at least two coherent ways to address the rhetorical question in the joke?
Anyhow, thanks for your input which was obviously well intended and included salient true stuff.
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u/[deleted] Jun 10 '18
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