Probability question: names in hats

[robvalue]

To put it another way:

To "win", you have to make two successful pulls. You have to pull a 2 from the 2 and a 3; then you have to pull the 1 from the remaining 1 and 3. That's two 50% shots you have to win. Overall 25%.

If you pick wrong first (3), with 50% chance, you lose. The game is over; but anyhow the only combination left is 3, 1, 2.

If you pick a 2 first but then miss and pull a 3, you lose; that's two 50% picks so 25%. Total 75% chance to lose.