Possibility Storm reads that when you cast a spell, you exile it, then exile cards from your library until you reveal a card of the same type. You may cast that revealed card without paying its mana cost. The word 'may' is critical — casting is optional under CR 609.2, which states that effects allowing you to cast a spell are permissive, not mandatory.
However, declining comes at a steep price. Whether you cast the revealed card or not, all exiled cards (including your original spell) are put on the bottom of your library in a random order. So if you decline, you lose your original spell and the revealed card — both get shuffled away — and you get nothing for your mana investment.
There is no way to 'undo' the trigger: once Possibility Storm's ability resolves and you choose not to cast the revealed card, the cleanup still happens. You cannot return to casting the original spell instead (CR 601.2 and the general rule that a replaced event cannot revert to its original form).
Concrete Example: You cast Counterspell. Possibility Storm triggers, exiling Counterspell. You reveal cards until you hit another instant — say, Lightning Bolt. You may cast Bolt for free, or decline. If you decline, both Counterspell and Bolt go to the bottom of your library. The spell you originally wanted to counter resolves normally.
This means declining is almost always worse than casting whatever is revealed, but the rules do give you the choice (CR 609.2, CR 112.3a).
Unofficial fan resource — not affiliated with or endorsed by Wizards of the Coast. Answers are AI-generated estimates grounded in the Comprehensive Rules and are not a substitute for an official judge. Verify anything match-critical.