A friend of mine is visiting a family in the UK, which we visited together 3 month ago. As little present he wants to bring a wine but he can't remember if they like dry or sweet. So he asked me. I said, "I'm 53% sure that they liked dry". Of course I wanted to express that I'm a little bit more confident that they like dry better than sweet.
He now objects that 0% confidence should mean that he doesn't gain any information from my statement (so it's 50/50 for him when he chooses the wine), while 100% means that he can just pick what I said and that will be correct.
However, what does 50% certainty of the statement "they liked dry" (50% instead of 53% because that is easier here) mean for the probability that the kind of wine he chooses will be correct?
Is it 75%? Is it 66%? Is it something else or doesn't the statement make sense in the first place?
I thought it might be a conditional probability (something like P(dry is correct | I said dry)), but I do not come to a good solution...
I would say that in a mathematical sens your statement has no meaning.
Indeed in math you can say : $x%$ of a population satisfy this property. This is equivalent of saying if I peek randomly (uniformly) among among the population I have probability $x/$ of peeking something that satisfy the property.
For your statement the population is not defined it thus has no mathematical meaning.
However It is used in common language, and I would say that the usual meaning is the one you used. But since it is not well defined, your friend is not wrong either :)