the library needs at least 15 people to sign up for an event in order to run it . Currently 3 people have signed up and the library expects 2 more people to sigh up each day . After how many days will the library be sure it can run the event?

The library currently has 3 people signed up, and it needs at least 15 people to run the event. Therefore, it still needs 15 - 3 = <<15-3=12>>12 more people to sign up.

Since the library expects 2 more people to sign up each day, it will take 12 / 2 = <<12/2=6>>6 more days for the library to be sure it can run the event.
So, after 6 days, the library will be sure it can run the event.