I activate a cursed scroll with a swamp and a badland in hand. If I name swamp and my opponent pick the badland, will cursed scroll deal damage?

Badlands
Color=Land Type=Land Cost=None ABUR(R)
Text(RV+errata): ~this~ is a mountain and a swamp in addition to its land type. [Oracle 2001/08/24]

This card is effectively of 3 land types. It is a "Badlands", a "Swamp", and a "Mountain". It is not a basic land, but it does count as being each of two basic land types for any cards that look for or count basic land types. [D'Angelo 2001/03/12]
This card is considered to be a Mountain and a Swamp even while in the graveyard, library, or anywhere else. The text applies even when it is not in play. [Jordan 2001/10/13]
The card works as if its text also has "{Tap}: Add {B} to your mana pool. ; {Tap}: Add {R} to your mana pool." [WotC Rules Team 2000/06/06]
Conversion changes the entire land to plains if it is a mountain. [WotC Rules Team 1998/02/01]

Cursed Scroll
Color=Artifact Type=Artifact Cost=1 TE(R)
Text(TE+errata): {3},{Tap}: Name a card. An opponent chooses a card at random from your hand. Reveal that card. If the card is the named card, ~this~ deals 2 damage to target creature or player. [Oracle 1999/07/21]

You choose a target creature or player on announcement. You choose the opponent and they pick a card from your hand during resolution. [D'Angelo 1999/06/01]
It does not target the opponent, but you still choose an opponent. [WotC Rules Team 1998/02/01]
If you have no cards in hand, you still have to name a card, but your opponent does not pick one. The card they chose cannot match the card you named, since they didn't get to pick one, so the Cursed Scroll does not deal any damage. [D'Angelo 1998/05/18]

Thanks!

Luc