The correct answer to the previous question was 2/3.
If you hadn't been given any information, the chance of at least one tails out of two flips is 3/4. The only way there would not be tails is if two heads were flipped – which most people know has only a 1/4 chance.
But you know what one coin was. This causes many people to just think about just the other coin, and reason it has a 50/50 chance of being heads or tails.
However, this reasoning ignores an important aspect of the probabilities involved: There are two ways that one heads and one tails can be flipped: heads first then tails, or tails first then heads. However, there is only one way to flip two heads – heads on the first flip, and heads on the second. Given at least one of the coins is heads, it is twice as likely for that scenario to have arisen where one of the coins is tails than where neither of them is.
If your friend had said she would only look at one coin and tell you if that coin was heads, then there would be only a 50/50 chance that the second coin is tails.
Does the explanation of the last question leave you unconvinced or unhappy?