The answer to "Painfully Easy" is false--but why? "Pop quiz, hotshot," the Villain said, "I've just flipped two coins. At least one of them is showing heads.
Ham Fisted
Don't you think this horse has been flogged enough already?
Paul Viney
Given that no one has correctly answered the problem, and the posted solution is false, no.
Ham Fisted
I really think 1 in 3 is right. There are 4 outcomes:
Joe Jewell
Why are each equally likely?
Ham Fisted
The rules of probability. An individual coin is as likely to be heads as it is tails. Thus each outcome has an equal probability of 1/4. Regardless of whether or not we through out some results, can you tell me why any of those outcomes should be less likely than another?
Joe Jewell
Why would you throw out only the two heads results?
Ham Fisted
From the problem statement: "At least one of these coins shows tails."
Joe Jewell
I'll hold off a little while longer.
Ham Fisted
If the answer depends upon the fact that he phrases the question differently, why is the initial answer of 1/3 wrong--before we even hear of the second (independent!!) set of flips?
Joe Jewell
Of course both flips are independent. And both coins are fair, and the villain always makes true statements.
Ham Fisted
(well except for the first threat involving the kitten. That was a false statement.)
Ham Fisted
I've personally seem many discussions of 'Painfully Easy' on this site alone. The same conclusion was reached each time. Assuming that 'one of the coins is heads' means 'at least one of the coins is heads', and there are no tricks in the working, then the chance of the other (i.e. both) coins being heads is 1/3. If anyone thinks differently please post your thoughts now.
David Clayworth
no tricks in the working -> no tricks in the wording
David Clayworth
David, please compare the problem statement of "painfully easy" with the problem statement that Joe linked to. There is a difference and it is no "trick of wording."
Ham Fisted
Sorry, Ham, not obvious to me.
David Clayworth
Martin Gardner wrote regarding the second-sibling paradox.
Ham Fisted
The correct answer then has to be that you can't tell. Depending on the procedure used, the answer could be 1/3, 1/2 or 1. If the villian acts randomly, then 1/3 is the correct answer. If the villian follows a preset pattern, then other answers are possible.
Paul Viney
Right. It's either 1/3 or poorly-asked.
Joe Jewell
I don't think you can form a coherent definition of what it means for the villain to "act randomly." If you mean picking one of the coins to reveal at random, then it's 1/2, unfortunately.
Ham Fisted
English is not my mother tongue, so I will try my best to explain my point of view.
JHY
You should have also said that both coins were lying flat and not on their side (however remote and improbable that was).
Tom Williams
I'm surprised that Ham Fisted says that both coins are fair. Although this assumption seems reasonable, the first question and answer sequence indicates otherwise. If the coins are fair, then the first answer must be correct.
May Bee
Ham Fisted is saying that the coins are fair, but the villain is not. Hence (s)he is the villain, I guess.
JHY
Are you people nuts?
ADA
ADA,
Tyler
Tyler,
Ham Fisted
Fog Creek Home |