Confused about twitter privacy?

[Fu]

my twitter account is private so that means anyone not following me can't see my tweets

if I tweet someone (eg celebrity, who's obviously not following me back) can they see that and what I tweeted them?

[Sara]

One thing you should know is that no matter what, Twitter is not a private social network. If you make a twitter account anyone can see it any time. It does not matter if it is private. That is the magic of the Internet. So yes, the celebrity will be able to see it. The only thing 'private' on twitter is the Direct Messages. But those are full of spam and stuff. It is like Twitter takes hold of your account and sends DM's to your friends without your consent.