A card is randomly drawn from a standard 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.
Either-or probability is determined by adding the individual probabilities.
Since there are only 3 other aces and 12 other hearts in the deck, 15/52.
To find the probability of winning a small prize, we need to determine the number of cards that would result in winning a small prize, and then divide it by the total number of possible outcomes.
There are 4 aces in a standard deck, and since any other ace would win a small prize, there are 4 - 1 = 3 possibilities for the type of ace that would win.
There are also 13 hearts in a standard deck, and since any heart (except for the ace of hearts) would also win a small prize, there are 13 - 1 = 12 possibilities for the type of heart that would win.
Therefore, the total number of cards that would result in winning a small prize is 3 + 12 = 15.
The total number of possible outcomes is the number of cards in a standard deck, which is 52.
Therefore, the probability of winning a small prize is 15/52.
Simplifying the fraction, the probability is 15/52, which cannot be further reduced. So, the probability of winning a small prize is 15/52.