So sorry about your chick. As others have said, things do happen when you have livestock - and the chick could have died whether it was with the others, or on its own, for a variety of reasons. Birds and animals can be horrible to each other, even babies, and if one is a bit weaker, they seem to know and peck it. It may be that the chick was weak, and the duck knew.
Its such a shame you had to go through this. Surely whoever sold you the chicks, should have realised it would be more sensible to start you off on older ones. I know no amount of saying these things happen will alter the guilt you feel, but they do happen, and all of us have been through it at one time or another. You still have the duck and other chick, so concentrate on them now, and enjoy watching them grow!!
Just keep an eye on that duck, in case it starts on the other chick
I have just had a look at your pics - didn't realise just how small the chicks were. I would not have ducks in with my small chicks, because ducks obviously grow a lot quicker, and will be bullies. I am sure they will grow up to be lovely birds though!!