I can believe someone can do it, not have faith at all.
a good example,
a man ties a tight rope a cross the Niagara Falls from the US to Canada.
he take a wheelbarrow, and walks it across that rope, a crowd gathers, and the man asked if they though he could take a person across it. No one really believed he could, so he puts in enough rock to make I the same weight as an average man, and walks it across a few times, he gets a rounding applause, so the man asked again, if anyone believed he could take a man across, they all excitedly say yes, they all BELIEVE he could do it
then he asked for volunteers silence, why? They all believed he could do it, so why would they not all do it? Because they did not have faith he would succeed, so they chose to deny his offer.
the same happens with Jesus offer of salvation,
many believe in him, (see James) but when it comes right down to it, and time to make a decision, they do not have faith in Jesus so although they may claim they have faith, their really do not, and their actions prove their lack of faith (actually it should be lack of action)
since their faith is dead, their lack of actions will support their lack of faith