Blue-eyed islanders with a stronger announcement

An island has 100 people with blue eyes and 100 with brown eyes. Everyone is a perfect logician. Nobody knows their own eye colour, and as far as anyone knows, an eye colour could be anything. There are no mirrors and nobody ever discusses eye colour. Every night a ferry takes away anyone who has worked out their own eye colour. One day a visitor tells the whole island: "I can see at least two people with blue eyes." (a) Who leaves, and on which night? (b) Suppose instead the visitor had taken each islander aside and said the same sentence in private, so that nobody knows who else heard it. What happens then?