A game show has 3 doors — one hides a prize, two are empty

A game show has 3 doors — one hides a prize, two are empty. You pick a door. The host (who knows where the prize is) opens one of the other two, revealing it is empty, and asks: switch, or stay? Ayush thinks the two remaining doors now each have an equal 50-50 chance, so switching gives no advantage. His teacher says switching is actually better. Who is right?

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More disagreements in Probability & Strategy Puzzles

A coin has been flipped 5 times in a row, landing heads every time In a lottery you pick 6 numbers Two dice are rolled together The forecast says a 50% chance of rain on Saturday and a 50% chance on Sunday Of two doors, one leads to freedom, the other to danger