Who can see it
Controls what friends see on your profile — not who is invited.
Visibility does not affect who is invited. An invitation always gets in. It controls what your connections who are not invited can see on your profile, and whether the event marks you as busy.
Public
Friends see the name, the time and how many people are going when they look at your profile.
Private
Friends see only that you are busy in that slot. No name, no venue, no guest count.
Hidden
Invisible to everyone except the people invited. It does not appear on your profile at all.
Hidden events and the busy warning
Hidden events are left out of the clash check as well. A friend picking a date will not be warned that you are busy, and you will not appear in their list of people with something on. Public and private events both count towards it.
Note — Private is the middle option: it keeps the details of the occasion to the guest list while still marking you as unavailable to friends choosing a date.
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