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Let's try to look at it this way.
You have, say 5 tickets, and only one is a winner.
Each ticket has 20% chance of being chosen. Although there are two possible outcomes, that's obvious, and the ticket you get is either winner or loser, chance of it being a winner is only 20%.
Let's say ticket 2 is the winner, here we have all possible cases:
Case 1: ticket 1, you lose
Case 2: ticket 2, you win
Case 3: ticket 3, you lose
Case 4: ticket 4, you lose
Case 5: ticket 5, you lose
Here you see that only 1/5 options are correct, or 20%.
Your fault is grouping all the losing tickets into one option and only a single one into the other. That way you make their chances equal when they're not.
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1+1=10
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