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.
12 hearts are not the ace. There are 3 other aces.
(12+3)/52 = 15/52 is the desired probability.
thanks alot steve!
To find the probability of winning a small prize, we need to determine the favorable outcomes and the total number of possible outcomes.
First, let's determine the favorable outcomes:
- There are 3 other aces in the deck (Ace of Clubs, Ace of Diamonds, Ace of Spades).
- There are 12 other hearts in the deck (2-10 of Hearts, Jack of Hearts, Queen of Hearts, King of Hearts).
So, there are a total of 3 + 12 = 15 favorable outcomes.
Next, let's determine the total number of possible outcomes:
A standard deck has 52 cards.
Therefore, the total number of possible outcomes is 52.
Now, we can calculate the probability of winning a small prize:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
= 15 / 52
= 15/52
Therefore, the probability of winning a small prize is 15/52 or simplified as 15/52.