By default, any health status update and activities, ailments, and life events will appear in your connection’s activity stream. If you're part of a group, your activity feed will also be seen be the group members and administrators. However, you can keep these events private by toggling the event to private before it’s submitted. 

Changing an existing event to private or deleting an event will remove it from your connections' and group's activity stream. 

If you no longer want to see someone's updates or would like to hide your updates from them, you can remove this connection.

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