Browsing the Internet, I stumbled upon a coin puzzle which I slightly shrank to emphasize my point:
Carl flipped two coins and was asked if at least one of the two coins landed “heads up”. He replied, “Yes. In fact the first coin I flipped landed heads up.” What is the chance that Carl’s coins both landed heads up?
The standard answer is 1/2, because there are only two possibilities for the coin flips: HH and HT. But how do we know that these possibilities are equally probable?
The answer depends on what we expect Carl to say when he flips two heads. My personal assumption is that Carl is a perfectionist and always volunteers extra information. If Carl gets two heads, I would expect him to say, “Yes. In fact both coins I flipped landed heads up.” In this case the answer to the puzzle is 0.
Another strange but reasonable assumption is that upon flipping two heads, there is an equal probability that Carl would say either, “Yes. In fact the first coin I flipped landed heads up;” or, “Yes. In fact the second coin I flipped landed heads up.” In this case, the answer to the puzzle is 1/3.
I could describe an assumption for Carl’s answering strategy that leads to the puzzle’s answer of 1/2, but it looks too artificial to me.
This puzzle is not well-defined, but unfortunately there are many versions of it floating around the Internet with incorrect solutions.Share: