A Possible Paradox of Hope?

A. One cannot hope without doubt.
B. To be without doubt is not to be hopeless.

Now, can A and B be true? And if not, which one of these propositions is incorrect?

To justify A - if one is certain of something, then there is no room to hope for it, one way or another. I am certain I'll receive a lovely slice of carrot cake. It cannot properly be said that I'm also hoping for it.

To justify B - if one is certain of achieving one's end, the pursuit of that end cannot be said to be hopeless. Quite the opposite. I'm certain I'll receive a lovely slice of carrot cake - hardly a hopeless situation if carrot cake is my aim!

Now, I can see two immediate ways of tackling this. The first is to say that certainty of a positive outcome, is in a sense, a kind of super-hope, beyond hope. One might recompose it as follows:

A. If I have a full pint, it can't properly be said that I have a half pint.
B. If I have a full pint, I could hardly complain that I'm lacking for a half pint.

Now, I want to shy away from this - I think it's crude. It possibly even amounts to: half a hope + half a hope = blind optimism. The idea that the difference between hope and 'optimistic certainty' is simply quantitative does not seem to my mind helpful. Though it must be said that optimistic certainty precludes hoping, without make one hopeless.

Which leads to the second way out - a distinction between the "act" of hoping/despairing and the disposition of hopefulness/hopelessness. We might want to put it like this:

(i) There's no carrot cake to be had, I cannot hope for it. (hopelessness)
(ii) I am certain to have carrot cake, I need not hope for it. (optimistic certainty)