Scout Willis Sentenced for Underage Drinking, Fake ID

7/31/2012 7:45 AM PDT

Scout Willis -- Sentenced for Underage Drinking, Fake ID

Breaking News
Demi Moore and Bruce Willis' 21-year-old daughter Scout has finally been punished for drinking beer while underage in NYC and possessing a fake ID ... but she won't be going to jail. 

Long story short -- Scout's getting off pretty easy ... she worked out a deal with prosecutors in which they agreed to dismiss the case entirely if she completes 2 days of community service and stays out of trouble for 6 months.

As we previously reported, Scout was arrested back in June after allegedly drinking a Pakistani beer in Union Square. She was 20 at the time.

When confronted by police, Scout allegedly handed over a fake ID saying she was "Katherine Kelly." She eventually admitted the ID wasn't hers.

Scout was initially booked for open container and criminal impersonation.

According to the NY Post, Scout's clean record and outstanding grades at Brown University scored points with prosecutors ... who agreed she doesn't deserve a harsh punishment, like jail.