There are four possible outcomes in this game: winning $1, winning $5, winning $10, or winning $0.
The probability of winning $1is the probability of drawing one of the 11 hearts that are not the ace of hearts. There are 52 cards in the deck, so the probability of drawing any one of them is 1/52. However, there are 11 hearts that win $1, so the probability of winning $1 is:
P(W = $1 ) = 11/52
The probability of winning $5 is the probability of drawing the ace of hearts, which is 1/52.
P(W = $5) = 1/52
The probability of winning $10 is the probability of drawing the king of spades, which is also 1/52.
P(W = $10) = 1/52
The probability of winning $0 is the probability of drawing any other card, which is 39/52.
P(W = $0) = 39/52