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How do I create a probability model?

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You don't state if you put the card back into the deck after each attampt or not, and if there are Jokers in the deck or not (or only 52 cards of 13 in each of 4 suits). If yes (cards are reinserted into the deck and it's a standard deck of 52 with no jokers), then you have a 1/4 chance of winning $5, a 1/4 chance of winning $10, and a 1/52 chance of winning $20. But if you DON'T replace the card after any attempt, then the odds depend on what you have already pulled, and can quickly get complicated... :-)