Balloon Pressure

1. The problem statement, all variables and given/known data
We were given homework to explain how this balloon pressure experiment works. You basically take a plastic bottle and make a small hole in it near the base. You then push a balloon in through the top and pull it over the bottle opening. You then blow it up so that it inflates inside the bottle. You then immediately plug the hole you made with your finger and it remains inflated in the bottle despite the balloon being open to the atmosphere. We have to discuss the pressure:

Inside the bottle
Outside the bottle
Inside the balloon

2. Relevant equations


3. The attempt at a solution
I have read up online which says that the pressure inside the bottle will be lower as air is pushed out of the bottle as you inflate it. The pressure outside the bottle is higher which keeps it inflated. but when thinking about the pressure inside the balloon I don’t understand why it stays inflated and no-one seems to mention pressure inside the balloon online. The pressure inside the balloon surely must be greater than outside the balloon. In order to blow up a normal balloon apparently you need 1 psi pressure to overcome the elastic forces of the balloon (i.e. a normal balloon has a higher pressure inside it). So if the air inside the balloon is greater than outside the balloon shouldn’t it deflate regardless of whether the pressure inside the bottle is lower?

Thanks for any guidance offered

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