Painfully easy I may be late on this, but the solution's wrong.
Andy West
He didn't say "the first one was heads"; he said "one of them was heads".
Paul Brinkley
I am damn sure the solution is wrong. My main argument against the posted solution is called "The Monte Carlo Fallacy." Go to http://gncurtis.home.texas.net/gamblers.html this will fully explain the fallacy
jj
The real question, which is disguised within the scenario, is, "What is the probability getting two heads?" The statement, "one of the coins came up heads," means ONLY that TT did not happen.
Chad Hulbert
Or if you prefer, consider this a conditional probability: What is the probability of getting two heads given one coin is heads?
Chad Hulbert
If you consider the opposite case, you can see why the odds are not 50-50, as classical independent coin-flipping logic would suggest.
Chris Farmer
Restating the problem: I flip two coins, and then tell you that one of them is heads. What's the probability that they are both heads?
Jim Lyon
"1. If I decide that I'll tell you that one of them is heads whenever that's true, then the odds that both are heads is 1/3."
Chad Hulbert
I'm not sure that I get your distinction between "odds" and "probability" -- I've used the words interchangably. While there are formal mathematical definitions of probability, the simplest intuitive definition is that if we repeated the experiment many times, what fraction of the time would we get the desired outcome.
Jim Lyon
I will concede that 'odds' and 'probability' are often used (incorrectly) interchangably in common speech, however in forums such as this, where we're talkin' statistics, the words are not ambiguous and have precise meanings.
Chad Hulbert
Just goes to show how confusing probability can be.
Andy West
Andy,
Chad Hulbert
A strong argument could be said that the probability of the other coin being heads is 0. After all the flipper said neither of "both coins came up heads" or "at least one coin came up heads" -- he said "one of the coins came up heads" -- i.e. "exactly one of the coins came up heads" by a standard pragmatic reading.
Jonathan Segal
Chad,
Andy West
"The actual question was (to paraphrase) 'I toss two coins, one is a head, what is the probability of the other being a head' To which the answer is 1/2, since the two events are independent."
Paul Brinkley
Andy,
Andy Shyne
Andy & Paul,
Andy West
I disagree with the posted answer.
Steve Barbour
Arrrgh. Here we go again. From the top, once more...
Paul Brinkley
Actually, I'll concede that you're right...but (you knew that was coming, right?)...
Steve Barbour
"There are only 3 possible combinations of our coins, since as the question is worded we have no way to distinguish the coins from each other. [...] So the combinations are TT, HH, or HT/TH, but the TH/HT outcome is twice as likely to occur."
Paul Brinkley
Yep (I thought I already agreed with that part).
Steve Barbour
"And the part that irritates me...if you know which coin is heads, then the chance of the other one being heads appears to be 1/2."
Paul Brinkley
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