When I first tried to inflate the balloon it was impossible. This was because the bottle is enclosed and inside air already occupied all the space. So when we tried to blow up the balloon there was no room for the balloon to inflate and grow.
The second time I tired to blow up the balloon the balloon inflated and easily expanded. This occurred because the air inside the bottle was pushed out the exit hole as the balloon inflated. When I placed my thumb over the hole once the balloon was inflated it stayed that way because we stopped the air from escaping. Once my thumb was removed, air from outside the bottle came
back in through the hole as the balloon deflated and retracted. This forced the air inside the balloon out through the mouth of the bottle.
If the hole is then plugged, the balloon stays inflated even when the mouth is removed. This is because the high pressure air in the balloon pushes outward harder than the low pressure air in the bottle. The air in the balloon pushes out against the walls, keeping it inflated. When the hole is unplugged, air flows back into the bottle. The air pressure in the bottle increases and collapses the balloon.