Was "The Necklace" believable? Give two supportive details to show that it was or was not.

Maupassant, the author of "The Necklace," is considered a
naturalist, which is a kicked up version of realism.  As such, he attempts to depict
reality or actuality, with an eye on his character's plight, particularly as
he/she contends with forces beyond control.  As such, "The Necklace" is certainly
intended to be realistic.

To examine it to answer your
question, one could look at what might possibly be seen and labeled a coincidence (which
doesn't work well in traditional fiction): the loss of the necklace.  There probably
isn't any good reason for doubting the veracity of a woman becoming so involved in her
situation and surroundings that she loses her necklace and isn't aware of it.  That's
plausible, and plausibility is the usual test for coincidence.  If something is
plausible, it's not a coincidence.

I recently started my
car, moved it into my driveway, shut it off and then cleaned the snow off of it.  A few
minutes later the car key was not in my pocket.  I looked for it and never found it.  I
didn't at first realize it was lost and couldn't find it once I did.  Mathilde's loss of
the necklace is plausible.

My anecdote also leads us to a
second point:  not only is the loss of the necklace plausible, but not being able to
find it is also realistic.

Just to throw in a third point
in case you need it, Mathilde's not even thinking of the possibility that the necklace
is fake is also plausible--maybe not for a wealthy woman who knows jewelry well and owns
plenty of it, but for a woman of Mathilde's economic class it is.  The thought never
crosses her mind.  She is inexperienced in the ways of the
wealthy. 

That final point, by the way, plays to the
naturalistic aspect of the story.  Mathilde is "out of her league," as they say.  She
is trapped by a situation that is out of her control.