"Probably" is more than one bit, not less, no? It conveys both uncertainty and an opinion on the answer.
"Is this tree deciduous?"
"Yes" - one bit
"Is this tree evergreen?"
"Probably" - one bit (they don't know), another bit (their guess)
But I'm way off any formal understanding of this, and it can be rigorously defined.
Meta comment: "half a bit" was clearly a joke, and so was my response; now I'm taking your reply at face value and debating it seriously, while admitting that I haven't got anything close to firm enough ground under me to actually debate it :)
I meant based on definition of a bit as "a yes or no answer to a single unambiguous question".
"Umm..." definitely carries some kind of information, but it doesn't actually help answer the question.
Based on the information theoretic definition of entropy we'd need to go from 50:50 to 89% certainty to get half a bit of information, and I'd probably qualify 89% certainty as "probably"
"Is this tree deciduous?" "Yes" - one bit
"Is this tree evergreen?" "Probably" - one bit (they don't know), another bit (their guess)
But I'm way off any formal understanding of this, and it can be rigorously defined.
Meta comment: "half a bit" was clearly a joke, and so was my response; now I'm taking your reply at face value and debating it seriously, while admitting that I haven't got anything close to firm enough ground under me to actually debate it :)