A card is randomly drawn from a standard $52$-card deck. an ace of hearts wins the grand prize; any other ace or heart wins a small prize. what is the probability of winning a small prize? express your answer as a common fraction. assume that a grand prize winner does not also win a small prize

In a standard 52 card deck, there are:

ace = 4

hearts = 13

where one of the hearts is an ace (hence there is a connection)

Since the major prize is an ace of hearts, therefore the minor prizes are selected from the below cards:

ace = 3

hearts = 12

We can see that both is decreased by 1 since the major prize was an ace and a heart at the same time.

Therefore the total number of cards which can gain a minor prize is now:

3 + 12 = 15

Therefore the probability of winning the minor prize from the 52 card deck is:

Probability = 15 / 52

Probability = 0.2885

Hence there is a 0.2885 chance or 28.85% chance that the minor prize is won.