When the second ability resolves, first the active player chooses a card to discard, then the nonactive player chooses, then all chosen cards are discarded at the same time. No one sees what the other players are discarding before deciding which cards to discard.
Random a card of Magic: The Gathering (MTG), but you can also roll the D20 dice, random a Planeswalker, have fun with the random rules and more.