Events have several different privacy settings available to the host:
Public: Anyone can join and be added to the event guest list without receiving an invitation or being approved by a host. Anyone can see the event description, photos, Wall posts and videos.
Friends of Guests: Friends of a host and guests can join and be added to the event guest list without receiving an invitation or being approved by a host. They can also see the event description, photos, Wall posts and videos. Once a friend of the host has joined, their friends will also be able to join the event. Stories about the event will appear in friends' News Feeds.
Invite Only: These events can only be seen by people who have received invitations and can't be found in public search results. People who haven't been invited can't view the event description, Wall or photos.
By clicking More Options in the event creation window, the host of an invite only event can choose whether or not to allow guests to:
Invite additional friends to the event
Tag the event as their location
See the guest list
Group Only: Group events are created within a group by a member or admin. The visibility of the event depends on the privacy setting of the group. Events created within open groups are visible to everyone and will appear in search results, but only group members can RSVP to these events. Events created within closed or secret groups are not visible or accessible to people outside of the group.
You should use the new Groups functionality to achieve this.
Create a group under the same name as your page and think of it as an inner circle to your more dedicated fans. You will then be able to invite group members to the event.
Pages are meant to provide information without being a nuisance to the follower. It is basically an extension of a business or celebrity. The 'fans' term was dropped and replaced with the 'like' term. Users 'like' your page they are not friends/members of your page. It can be a passing penchant. I can decide to like your page today and not like it tomorrow. Hence the way I see it , Facebook Pages can never contact me outside of Facebook i.e. by mail . Potential spam (click-jacking,liking useless pages) headache avoided.
If you really want to use your page you will need to focus on getting more attention to your events by hooking up some fbml and a tab as the default page instead of the wall. Also look into your insights and decide when is the best time/day to update your followers.
Best Answer
It depends on the privacy settings of the event.
From the Facebook help center