A Basic Question about brut force key recovery attack

Hello
I am now to the area and trying to
learn more about Cryptography

I have a very basic question, can someone
please help me out

Now I see that the longer the key being using for
encryption the better lets take a 128 bit key used with AES e.g. 2 to the power
of 128

first question (and sorry if these seem a bit basic)

I
assume the actual key is a128 long binary number e.g. a combination of 128 zeros
and ones, is this correct so far?

if so then I presume any of these bits
can be set to either a 0 or a 1
which would explain why I have 2 to the power
of 128 possible combinations (keys) correct so far?

Now when I watch
videos on the subject they always state that the longer the key the longer to
crack (every thing else being equal).

However, I am thinking of a large
box with physical keys and door lock to a house say. Now I have a few million
keys in my box, one of which fits the lock and the others do not.

I put
my hand in a grab a key at random and try it, well what happens if I just get
lucky and it is the second key I try out of the box of millions on
keys?

Basically this would mean it did not take me a few 1000 years to
find the key but a couple of minutes.

So is it true to say that a longer
key does not necessary mean it will take longer (luck of the draw), but rather
you are statistically less likely to get lucky the more keys you have to check?
so no matter how long the key you could still get lucky and find the right key
within a couple of tries?

Thank you very much
AAnotherUser